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# If sin $$\theta$$ = cos $$\theta$$, find $$\theta$$ between 0o and 360o...

### Question

If sin $$\theta$$ = cos $$\theta$$, find $$\theta$$ between 0o and 360o

### Options

A) 45o, 225o

B) 135o, 315o

C) 45o, 315o

D) 135o, 225o

The correct answer is C.

### Explanation:

sin $$\theta$$ = cos $$\theta$$ 0 $$\leq$$ $$\theta$$ $$\leq$$ 360o
The acute angle where sin $$\theta$$ = cos $$\theta$$ = 45o
But at the fourth Quadrant Cos $$\theta$$ = +ve
at the 4th quadrant, value with respect to Q is
(360 - Q) where Q = acute angle
(360 - 45) = 315o
The two solution are 45o, 315o

## Dicussion (1)

• sin $$\theta$$ = cos $$\theta$$ 0 $$\leq$$ $$\theta$$ $$\leq$$ 360o
The acute angle where sin $$\theta$$ = cos $$\theta$$ = 45o
But at the fourth Quadrant Cos $$\theta$$ = +ve
at the 4th quadrant, value with respect to Q is
(360 - Q) where Q = acute angle
(360 - 45) = 315o
The two solution are 45o, 315o