Question

Find the value of the

trig function
a. Cos Ɵ = 2/5 find Tan Ɵ
b. Cosec Ɵ = 7/3 find Cos Ɵ
c. Cot Ɵ = 4/3 find Sec Ɵ
d. Tan Ɵ = 3 find Cosec Ɵ

Answer 1

a.

cos θ = 2/5, tan θ = ?

• tan θ = sin θ / cos θ
• tan θ = √sin² θ / (2/5)
• tan θ= 5√(1 - cos²θ) / 2
• tan θ = 5√(1 - 4/25) / 2
• tan θ = 5√(21/25) / 2
• tan θ = √21 / 2

b.

cosec θ = 7/3, cos θ = ?

• cosec θ = 1/ sin θ
• cosec θ = 1/ √(1 - cos²θ)
• √(1 - cos²θ) = 1 / cosec θ
• 1 - cos²θ = (1 / (7/3))²
• cos²θ = 1 - 9 / 49
• cos²θ = 40/49
• cos θ = √40/49
• cos θ = 2√10/7

c.

cot θ = 4/3, sec θ = ?

• cot θ = cos θ / sin θ
• cos θ = cot θ * sin θ
• cos θ = 4/3 * √(1 - cos²θ)
• 9cos²θ = 16(1 - cos²θ)
• 25cos²θ = 16
• cos²θ = 16/25
• cos θ √16/25
• cos θ = 4/5
• sec θ = 1/ cos θ
• sec θ = 1/ (4/5)
• sec θ = 5/4

d.

tan θ = 3, cosec θ = ?

• sin²θ + cos²θ = 1
• 1 + cos²θ/sin²θ = 1/ sin²θ
• 1 + 1/tan²θ = cosec²θ
• 1 + 1/9 = cosec²θ
• cosec²θ = 10/9
• cosec θ = √(10/9)
• cosec θ = √10 / 3