Question #728ad

1 Answer
Dec 13, 2017

Use the properties of triangles to determine the side lengths for the function.

Explanation:

Using the known angles of triangles and the relationship of the sides to the trigonometric functions, we can calculate these values.
The angle of 315 is complementary to 45 (the sum to 360 - a full circle), so the sin will be the negative of the complementary angle.
45 degrees is one side of a right triangle with equal sides and angles. The sine is the ratio of the opposite side length to the hypotenuse. They hypotenuse squared is the sum of the two sides squared.
#1^2 + 1^2 = h^2#; #h^2 = 2#; #h = 1.414#

#sin(45) = 1/1.414 = 0.707#

#sin(315) = -0.707#

Similarly for the tangent of 600 - the real angle is just remainder from a multiple of 360. #600-360 = 240# Or, directly, a multiple of a 60-degree angle, so the tangent will be the same for 600 degrees or 60 degrees. We again have a right triangle with angles of 90, 60 and 30. If we construct a triangle we can measure or calculate the lengths. Use any size for desired accuracy. Mine was a 4cm short side with a resulting 7cm long side and a hypotenuse of 8cm.

Tangent is opposite side divided by adjacent side:
#tan(60) = 7/4 = 1.75#

Further refinement could be done in measuring the lengths to get the (calculator) value of 1.73.