Right Triangles
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The Pythagorean Theorem
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Special Right Triangles
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Basic Trigonometric Functions
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Solving Right Triangles
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Measuring Rotation
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Applying Trig Functions to Angles of Rotation
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Trigonometric Functions of Any Angle
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Relating Trigonometric Functions
Graphing Trigonometric Functions
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Radian Measure
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Applications of Radian Measure
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Circular Functions of Real Numbers
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Translating Sine and Cosine Functions
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Amplitude, Period and Frequency
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General Sinusoidal Graphs
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Graphing Tangent, Cotangent, Secant, and Cosecant
Trigonometric Identities and Equations
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Fundamental Identities
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Proving Identities
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Solving Trigonometric Equations
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Sum and Difference Identities
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Double Angle Identities
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Half-Angle Identities
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Products, Sums, Linear Combinations, and Applications
Inverse Trigonometric Functions
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Basic Inverse Trigonometric Functions
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Graphing Inverse Trigonometric Functions
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Inverse Trigonometric Properties
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Applications and Models
Triangles and Vectors
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The Law of Cosines
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Area of a Triangle
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The Law of Sines
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The Ambiguous Case
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General Solutions of Triangles
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Vectors
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Component Vectors
The Polar System
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Polar Coordinates
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Graphing Basic Polar Equations
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Converting Between Systems
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More with Polar Curves
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The Trigonometric Form of Complex Numbers
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The Product and Quotient Theorems
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De Moivre’s and the nth Root Theorems
Uncategorized Questions
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Question #77828
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What are the lengths of the sides of a scalene triangle with a 1 cm. incircle?
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Prove that #(1-sin2x)/(1-cosx)=-cosx#?
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Question #9b4c9
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Question #055a3
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Prove that #(tanx-cotx)/(tanx+cotx)=1-2cos^2x#?
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How do I prove that #1/(sec A+1)+1/(sec A-1)#=#2 csc A cot A# ?
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How do I prove the identity #tan theta sin theta + cos theta -= sec theta# ?
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Prove that sinxtanx+cosx=secx (where x is theta)?
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Question #936dc
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How so you prove:
#(sec^2(x)cot(x)-cot(x))/(tan(x)sin(x)+cos(x))=sin(x)#?
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Question #1dd55
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Question #776b1
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Question #54096
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Question #a30c3
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Question #a3292
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Question #a2179
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Four marbles of radius #3/8# inch are placed in a cylindrical container. The first three marbles fit snuggly with the fourth marble on top. The cylinder is then filled with water up to the top of the fourth marble. What is the volume of water?
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Question #8c8ad
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Given that #cos x =p# find an expression, in terms of #p#, for #tan^2 x#?
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How do I solve #2(sin x-cos x)=3(sin x+cos x)# ?
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Question #54481
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Question #3958e
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#4sin(2x)=tanx#, solve for x (for #0<=x<=360#). I'm getting 7 answers, but only 4 answers are listed, and they are between #0# and #180#. Can somebody solve this?
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#sin(2x)=2cos(2x)-1#, solve for #x# (#0<=x<=180#). Can somebody please solve this?
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#2cos(3x)=2+sin(3x)#, solve for #x# (#0<=x<=180#). solve this please?
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"After showing that #2sectheta-tantheta=3# can be written as #sqrt10cos(theta-18.4)=2#, solve for #theta# (#0<theta<360#)". I proved the first part, can somebody please solve for #theta#?
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The angle #theta# satisfies #tan(2theta)=sintheta#. Show that either #sintheta=0# or #2costheta=2cos^2theta-1# (i did this). Hence find the smallest possible value of #theta#?
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How do you factor #2x^2 - 3xy - 2y^2#?
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Question #02641
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Which quadrants should be considered when solving #cosx=(sqrt2)/4# for #0^@<=x<=360^@#, and why?
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Question #0b699
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Question #5e9cc
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Question #de479
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Question #5aa2c
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Question #a07f3
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To how many digits do you know #pi#?
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Question #bb0b9
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2cos^2x+sqrt(3)cosx=0
solution set: {pi/2, 3pi/2, 7pi/6, 5pi/6}
I can't figure out how to get those solutions?
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5sinx=5sqrt(3)cosx 0<x<2pi
What are all possible solutions in radians?
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Tanx=(-2sqrt3/3)sinx 0<x<2pi
What are all possible solutions?
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Question #4abc6
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Why use radians instead of degrees?
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5sinx=5sqrt3cosx 0<x<2pi
What are all possible solutions?
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Question #c45e4
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Question #8889f
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Question #a72dd
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Question #6bfad
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Question #509cd
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2sin^2x-9sinx+7=0
What's the solution set?
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Tanx=(2sqrt3/3)sinx
What are all solutions?
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Question #54a35
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Question #db9ce
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The lengths of two sides of a triangle are 12 ft and 13 ft. What is the range of possible lengths for the third side?
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In a triangle ABC, the measure of angle A is fifteen less than twice the measure of angle B. The measure of angle C equals the sum of the measures of angle A and angle B. What is the measure of angle B?
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A triangle has two sides equal in length and a third side 5 inches longer than half the length of each of the other two sides. If the perimeter of the triangle is 50 inches, how long is each side?
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What is the exact value of #tan(3pi)/8#?
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What is the value of cos 75°?
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Can the measures 7, 11, and 15 be side lengths of a triangle? If so, is the triangle acute, obtuse, or right?
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The angle as of a triangle are as follows: Angle A is the largest angle; its measure is twice the measure of Angle B. The measure of Angle C is 2 less than half the measure of Angle B. What is the measure of the three angles?
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How do you solve the triangle DEF, where, angle E is 144 degrees side e is 10.5m and side f is 12.5m?
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How do you verify # (3sinx-2cos^2x)/(2+sinx) = 2sinx -1#?
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An office building 55 ft tall casts a shadow 30 ft long. How tall is a person standing nearby who casts a shadow 3 ft long?
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The measure of an angle is nine times the measure of a supplementary angle. What ls the measure of each angle?
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An angle measures 70° more than the measure of a supplementary angle. What Is the measure of each angle?
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A skier is at the top of a mountain. His angle of depression looking down at the ski lodge is 54°25'28". If he rides the ski lift 8750 feet to the lodge, how far is the lodge from the base of the mountain?
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What is #csc# #(7pi)/6#?
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How do you verify #csc^2 θ + sec^2 θ = csc^2 θsec^2 θ#?
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The difference of two supplementary angles is 32 degrees. What are the angles?
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If #sin theta = -1/3#, and #180° < theta < 270°#, what is #tan theta#?
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Two door stops have cross-sections that are right triangles. They both have a 20° angle and the length of the side between the 90° and 20° angles are equal. Are the cross sections congruent?
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The measures of the angles of triangle XYZ are in the ratio 3:3:6. What are the measures of the angles?
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If #sin theta = - 3/5# and #180° < theta < 270°#, what is #tan 2theta#?
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A monument casts a 40-foot shadow. Adam is 6 feet tall and casts a 5-foot shadow. How tall is the monument?
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A triangle has sides of 3 and 8 units. The measurement of the longest side is missing. Tevin says that one possibility for the unknown side length is 15. Is this true?
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If the measure of #∠K# is 29 degrees and it is supplementary with #∠J#, what is the measure of #∠J#?
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Angles Q and R are complementary. What is #m∠R# if #m∠Q = 24°#?
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The length of a side of an equilateral triangle is 12. What is the length of the altitude in simplest radical form?
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The length of one leg of a right triangle is 3 and the length of the other leg is 5. What is the length of the hypotenuse?
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The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. What is the length of the other leg?
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Question #459f8
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Is a triangle with side lengths of #sqrt(12), sqrt(7), and sqrt(5)# a right triangle?
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Jacky has to repair his window so he used a ladder. He placed the ladder 12 feet from a window. The ladder reaches 14 feet up on the window. How long is the ladder?
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Two angles of a triangle are the same size. The third angle is 3 times as large as the first. How large are the angles?
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How do you verify? #(cos2x)/ (1+sin2x) =(1-tanx)/(1+tanx)#
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If the base angle of an isosceles triangle is 40°, what is the measure of its vertex angle?
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The measures of two angles of a triangle are 60 and 45. What kind of triangle is it?
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The length of the hypotenuse of a right triangle is 17 centimeters and the length of one of the legs is 8 centimeters. What is the number of centimeters in the length of the second leg?
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What is the hypotenuse of a triangle with legs 25 and 43?
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What are supplementary angles?
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If the measures of a triangle are #90°#, #55°#, and #3x + 5#, what is the value of #x#?
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The sides of the base of the largest pyramid, Khufu, has length 755 ft. The height of Khufu was originally 482 ft but is now 450 ft. What is the length of the slope of a side of the pyramid at its original size and its present size?
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A minimum value of a sinusoidal Function is at #(pi/4, 3)#. The nearest maximum value to the right of this point is at #((7pi)/12, 7)#. What is the equation of this function?
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How/Why do you get the solutions to a trigonometry equation with multiple angles?
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Question #277b3
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Question #47b9f
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How do you divide #(20x^4+(5-12i)x^3-(25+3i)x^2+15ix)/(5x-3i)# ?
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What is the hypotenuse of a triangle with legs of #5# and #9#?
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Question #d1a14
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Question #7f1a4