the-value-of-in-the-range-0-90-for-which-sin-cos-is-

Question Number 33413 by Rio Mike last updated on 15/Apr/18

t h e v a l u e o f θ, i n t h e r a n g e 0 ° ⩽ θ ⩽ 90 °

f o r w h i c h s i n θ = c o s θ i s \dots ?

Commented by Rasheed.Sindhi last updated on 16/Apr/18

\sin θ = \cos (90 - θ)

θ = 90 - θ

2 θ = 90

θ = 45

\sin 45 = \cos 45

Commented by abdo imad last updated on 17/Apr/18

s i n θ = c o s θ \Leftrightarrow s i n θ = s i n (\frac{π}{2} - θ) \Leftrightarrow θ = \frac{π}{2} - θ + 2 k π o r

θ = π - (\frac{π}{2} - θ) + 2 k π (k \in Z) \Leftrightarrow 2 θ = \frac{π}{2} + 2 k π o r θ = \frac{π}{2} + θ + 2 k π

\Leftrightarrow θ = \frac{π}{4} + k π b u t w e h a v e 0 ⩽ θ ⩽ \frac{π}{2} \Rightarrow 0 ⩽ \frac{π}{4} + k π ⩽ \frac{π}{2}

\Rightarrow 0 ⩽ \frac{1}{4} + k ⩽ \frac{1}{2} \Rightarrow - \frac{1}{4} ⩽ k ⩽ \frac{1}{4} \Rightarrow k = 0 \Rightarrow θ = \frac{π}{4} .