Question

if 2sin theta =1, the the value of angle theta is​

Answer 1

Answer: $\rm \theta = 45^{\degree}$

Explanation: Since it is given that,

$\rm 2 \ sin \ \theta = 1$

$\rm \implies sin \ \theta = \dfrac{1}{2}$

$\rm \implies sin \ \theta = sin \ 45^{\degree}$

$\rm \implies \theta = 45^{\degree}$.

More:

• $\rm sin \ (\theta - 90^{\degree}) = cos \theta; tan \ (\theta - 90^{\degree}) = cot \ \theta; cosec \ (\theta - 90^{\degree}) = sec \ \theta$ (and vice versa).
• Identities:

1. $\rm sin^2 \ \theta + cos^2 \ \theta = 1$
2. $\rm sec^2 \ \theta - tan^2 \theta = 1$
3. $\rm csc^2 \ \theta + cot^2 \ \theta = 1$

Derivatives:

• $\rm sin \ \theta - cos \ \theta = \dfrac{1}{sin \ \theta + cos \ \theta}$
• $\rm sec \ \theta + tan \ \theta = \dfrac{1}{sec \ \theta - tan \ \theta}$
• $\rm csc \ \theta + cot \ \theta = \dfrac{1}{csc \ \theta - cot \ \theta}$