Question

The point (5, −2) is on the terminal ray of angle θ, which is in standard position. Without evaluating, explain how you would find the values of the six trigonometric functions.

Answer 1

Answer:

Plot the point (5, –2) and draw a line from the point to the x-axis to make a right triangle.

Use the Pythagorean theorem to find the length of the hypotenuse.

Use the definition of each trigonometric function to find the values.

Determine the appropriate sign for each function, using the fact that the terminal side is in Quadrant IV.

Step-by-step explanation:

Answer 2

1. Check the picture attached.

let P, M, N be the points :P(5, -2), M(5, 0), N(0, -2)

ABP is the angle with measure ∅, where BA is the initial ray and BP the terminal ray.

2. m(PNM)=∅ as can be easily checked

In triangle PNM, NP=5, PM=2 and NM=$\sqrt{ 5^{2} + 2^{2} }= \sqrt{25+4}= \sqrt{29}$ units


3. let opp=opposite side, adj=adjecent side, hyp=hypothenuse

sin ∅ = opp/hyp=$\frac{2}{\sqrt{29}}$

cos ∅ = adj/hyp=$\frac{5}{\sqrt{29}}$

tan ∅ = opp/adj=2/5

cot ∅ = adj/opp=5/2

sec ∅ = hyp/adj=$\frac{\sqrt{29}}{5}$

csc ∅ = hyp/opp=$\frac{\sqrt{29}}{2}$