Question

1. Find the value of

sec Θ if tan Θ = -2 90° ≤ Θ ≤ 180°

a. - sqrt(5)
b. sqrt(5)
c. -5
d. 5

2. Find the value of cos Θ if sec Θ = s/3 270° ≤ Θ ≤ 360°

cos =

3. Find the value of
csc Θ of cos Θ = -3/5 180° ≤ Θ ≤ 270°
csc =

Answer 1

9514 1404 393

Answer:

1. -√5
2. 3/5
3. -4/5

Explanation:

The relevant relations are ...

sec = ±√(tan² +1)

cos = 1/sec

csc = 1/sin = ±1/√(1 -cos²)

Sine and Cosecant are positive in quadrants I and II. Cosine and Secant are positive in quadrants I and IV.

__

1. sec(θ) = -√((-2)² +1) = -√5

2. cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5

3. csc(θ) = -1/√(1 -(-3/5)²) = -√(16/25) = -4/5