Question

1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta).

2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta) and tan(theta).

3. Let (theta) be an angle in quadrant II such that csc(theta)=7/4. Find the exact values of tan(theta) and cos(theta).
4. Use a cofunction to write an expression equal to csc(3pi/8).


Thank You <3

Answer 1

1. (-7,4) is in quadrants II,
so x=-7, y = 4
by Pythagoras, r = √(49 = 16) = √65

sinØ = y/r = 4/√65
cscØ = r/y = √65/4
cotØ = x/y = -7/4

2. since sinØ = -2/5 and Ø is in IV,
y = -2, r = 5, then x^2 + 4 = 25
x = √21

etc.

can you finish the rest?