Question

If 0° ≤ θ ≤ 90° and cosθ =
11
15
, what is the value of sin (90° - θ)?

Answer 1

cos Ф = 11/5. Calculate the value of angle Ф:

cos⁻¹(11/15) = 42.83342807°

sin(90-Ф) =sin (90-42.83342807) = sin(47.16657193) = 11/5

So cos Ф = sin(90-Ф) = 11/15

Answer 2

Answer:

$sin (90 - \theta) \approx 0.73$

Step-by-step explanation:

The given expression is

$cos\theta =\frac{11}{15}$

According to trigonometric identities

$sin(90-\theta)=cos\theta$

We also can find the angle using the given expression and then replace it in the sin expression

$cos\theta=\frac{11}{15}\\ \theta=cos^{-1}(\frac{11}{15})\approx 42.83$

Now, we find the answer for the sin expression:

$sin (90 - \theta)=sin(90-42.83)=sin(47.17)\approx0.73$

Again, the faster way to solve this is by using the identity:

If $sin(90-\theta)=cos\theta$ and $cos\theta =\frac{11}{15}$, then $sin(90-\theta)=\frac{11}{15}$