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

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

Explanation:

The given expression is

`cos\theta =(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=(11)/(15)\\ \theta=cos^(-1)((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 =(11)/(15)`, then
`sin(90-\theta)=(11)/(15)`