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How to solve these trigonometric equations?

+4 votes

Please show step by step how you solved the value of theta :)

1. cos²Ө = 1 - 2sin²Ө

2. 2(sec²Ө + tan²Ө) = 11

asked Jan 25, 2013 in TRIGONOMETRY by potatoes Rookie

1 Answer

+5 votes
 
Best answer

1. cos²Ө = 1 - 2sin²Ө
 

Recall Pythagorean identity: sin2 θ + cos2 θ = 1 ---->  cos2 θ = 1-sin2θ

1-sin²Ө = 1 - 2sin²Ө

sin²Ө=0

sinӨ=0

Ө=nπ

Where n=0,1,2,3...............

2. 2(sec²Ө + tan²Ө) = 11

Recall trignometric identity: sec2 θ - tan2 θ = 1 ---->  1 + tan2 θ = sec2θ

2(1 + tan2 θ + tan²Ө) = 11

(1 +2 tan2 θ) = 11/2

2 tan2 θ=9/2

tan2 θ=9/4

tanθ=3/2

Using calculator

θ=56.3

I hope it helps!!!

 

 

answered Jan 26, 2013 by bradely Mentor
selected Jan 26, 2013 by potatoes
You are correct...
1
cos²Ө = 1 - 2sin²Ө
Ө=nπ, where n is the set of integers.

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