Trigonometry

Featured Answers

Right Triangles

• The Pythagorean Theorem
• Special Right Triangles
• Basic Trigonometric Functions
• Solving Right Triangles
• Measuring Rotation
• Applying Trig Functions to Angles of Rotation
• Trigonometric Functions of Any Angle
• Relating Trigonometric Functions

Graphing Trigonometric Functions

• Radian Measure
• Applications of Radian Measure
• Circular Functions of Real Numbers
• Translating Sine and Cosine Functions
• Amplitude, Period and Frequency
• General Sinusoidal Graphs
• Graphing Tangent, Cotangent, Secant, and Cosecant

Trigonometric Identities and Equations

• Fundamental Identities
• Proving Identities
• Solving Trigonometric Equations
• Sum and Difference Identities
• Double Angle Identities
• Half-Angle Identities
• Products, Sums, Linear Combinations, and Applications

Inverse Trigonometric Functions

• Basic Inverse Trigonometric Functions
• Graphing Inverse Trigonometric Functions
• Inverse Trigonometric Properties
• Applications and Models

Triangles and Vectors

• The Law of Cosines
• Area of a Triangle
• The Law of Sines
• The Ambiguous Case
• General Solutions of Triangles
• Vectors
• Component Vectors

The Polar System

• Polar Coordinates
• Graphing Basic Polar Equations
• Converting Between Systems
• More with Polar Curves
• The Trigonometric Form of Complex Numbers
• The Product and Quotient Theorems
• De Moivre’s and the nth Root Theorems

Uncategorized Questions

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• How do you identify the vertical and horizontal translations of sine and cosine from a graph and an equation?
• If you have a SSA angle case with two possible solutions, how can you check both solutions to make sure they are correct?
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• Is time real?
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• Find the exact value of: csc^2(17pi/4) How do I do problems with the sin, cos, tan...etc raised to the power of 2?
• Find the exact value of sin^3 3645° Do I go around the circle 10 times? is there an easier way to do this?
• Is there an easy way i can find the related acute angle(reference angle) when give any degree? If not then can u tell me a method that is proper so that i can do good on reference angle
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• Determine two other angles that have the same trigonometric function value: a) sin 47 b) cos 56. For a, the value is 0.731 and for b) it's 0.559?
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• I need help how do i determine the phase shift when i am given a graph, i need it for sinusoidal function. I know how to figure everything except phase shift(d)?
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• How do you use hyperbolic trigonometric functions?
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• If #x = tan(1)#, #y = tan(2)# and #z = tan(3)#, then how do you place #x, y, z# in decreasing order?
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• How do you graph #y=-tan(x-pi/2)#?
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• What is the trig unit circle? How does the trig circle define the trig functions?
• What is the relation ship between sin x and sin (180 - x)? between sin x and sin (180 + x)?
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• How do you graph #y = cos(90-A)# as sinA?
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• In which quadrant is #(110012pi)/11# ?
• How do the double and treble angle formulas for #sin# and #cos# relate to powers of #cos theta + i sin theta# ?
• A portable conveyor user by roofers is 11.0m long. The angle between the conveyor and the ground can be adjusted from 30° to 70°. What is the range of heights that the conveyor can reach?
• Given tan x tan y = p and cos(x+y)=q .Show that sin x sin y =(pq)/(1-q) and cos(x-y)= (q(1+p))/(1-p) ?
• If x a third quadrant angle and y an acute angle such that cos x=-(3/5) and sec y= (3/2) ,find the exact value of sin(x-y) , exact value of tan(x-y) and quadrant containing (x-y)?
• Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?
• Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?
• Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?
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• What point is equidistant from #(0, 0)#, #(3, 0)# and #(6, 0)# ?
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• Verify the following identities (a) tan 3x =[ tan x(3-tan²x]/(1-3tan²x)?
• Write the following products as a sum or difference (a)sin 2xcos3x (b) cos 5x cos 3x (c)sin4xsin2x (d)cos3xsin6x ?
• Write the following sums or differences as a product (a)sin 2x + sin 3x (b)cos 5x- cos 3x (c)sin 4x -sin 2x (d)cos 3x + cos 6x?
• Verify the following identities: (a) #2sin^2(2x) + cos4x=1# (b) #tanx+co x =2sec2x# (c) #tan3x =[tanx(3-tan^2x)]/ (1-3tan^2x)#?
• Find all exact angles in the interval [0,2pi] that satisfy the following equations. (a)cos x +cos 2x =0 (b) cos 2x=-0.5 (c)√(12) + 2 tan (x/2)=0 (c)cos 2x=-0.5 (d)sin (2x - (pi/2))= -0.5 ?
• Find all exact angles x in the interval [0,360°] that satisfy the following equations (a)2tan²x +5tanx-3=0 (b)6cosx=secx +1 (c) 3cos x = cot x (d)csc x tan x = 5?
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• Write #sin x +sin 3x# as a product. Hence,find all angles #x# in the interval#[0,2pi]# that satisfy #sin x +sin 3x - cos x =0#?
• Find the maximum and minimum values of the following functions (a)#y= 3 sin x+ 4 cos x +2# (b) #y= 6cos x - 4 sin x -2#?
• Express sin x - 3 cos x in the form of r sin (x-y) with r>0 and 0< y < (pi/2) ?
• Find the general solutions (a)3 cos x - 4 sin x = 2 (b) 3 cos x + 4 sin x =5 (c) 5 sin x - 12 cos x =13 (d) 2 sin 2x + cos 2x = 2?
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• 4sinx cosx - 2√3 sin x + 2√3 cos x - 3=0 find all the solution?
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• We have a triangle ABC. Point D lies on BC and point E lies on the side AB. We know that, AC = BD , AD = AE , AB2 = (AC)(BC). How can you prove that angle BAD = angle CEA ?
• Find all the solutions for #sinx=a#?
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• How do I prove that #(3-6 cos^2 x)/(sin x- cos x)# = 3(sin x + cos x)?
• How do I prove that #sin^2x# + #tan^2xsin^2x# = #tan^2x# ?
• How do I solve #sec^2x# + 2 #tan^2x# =4?
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• How do I solve #4 sin x + 9 cos x = 0# for #0 < x < 360# ?
• A 40-foot television antenna stands on top of a building. From a point on the ground, the angles of elevation of the top and bottom of the antenna, respectively, have measurements of 56 degrees and 42 degrees. How tall is the building?
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• How do I solve #3 sin x+2 tan x=0# for #0<=x<=360# ?
• How do I solve #3 sin x+2 tan x=0# for #0°<x<360°# ?
• How do I solve #2 csc (z+pi/4)=5# for #0<=z<=6# radians?
• In triangle ABC, how do you solve the right triangle given Side AB=17 Side BC=22?
• How do I solve #2 cos^2 x-sin x+1=0# for #0° <=x<=360°#?
• How do you solve #tan^2x-2sec x+1=0# for #0°<=x<=360°# ?
• Question #e38b9
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