Three trigonometric functions for a given angle are shown below. sin theta = -77/85, cos theta=36/85 tan theta=77/36 What are th

Question

3 years ago

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Three trigonometric functions for a given angle are shown below. sin theta = -77/85, cos theta=36/85 tan theta=77/36 What are th

e coordinates of point (x, y) on the terminal ray of angle theta assuming that the values above were not simplified?
A) (-77,-36)
B)(-77,36)
C) (-36,77)
D) (36, -77)

Mathematics

2 answers:

Marizza181 [45] · Answer 1 · 2021-12-29T08:44:57+03:00

Answer:

The correct option is D.

Step-by-step explanation:

It is given that

$\sin \theta =\frac{-77}{85}$

$\cos \theta =\frac{36}{85}$

The angle of terminal ray is θ, it means the angle between x-axis and terminal ray is θ.

$\sin \theta =\frac{perpendicular}{hypotenuse}$

$\cos \theta =\frac{base}{hypotenuse}$

Therefore the length of perpendicular is 77 and the base of the triangle is 36.

Since sinθ is negative and cosθ is positive, it means point must be lies on fourth quadrant because in fourth quadrant cosine in positive but sine is negative.

The point of terminal ray is (base, perpendicular) and the sign are used according to the quadrant.

Therefore the point of terminal ray is (36,-77) because in fourth quadrant x is positive but y is negative. Option D is correct.