Question

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

Answer 1

Answer:

The value of $\sin (90-\theta)$ is:

$\dfrac{11}{15}$

Step-by-step explanation:

We are given an angle  "Theta" or θ which lie in the first quadrant i.e.  0°≤θ≤90°

Also we are given cosine of angle theta as:

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

Now we are asked to find the value of:

$\sin (90-\theta)$

We know that:

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

( Since, the conversion of the angle 90-θ will remain in the same first quadrant

since, 0°≤θ≤90°

-90°≤-θ≤0°

90°-90°≤90°-θ≤90°

Hence,   0°≤90°-θ≤90°

    and as both cosine and sine function are positive in the first quadrant,

so, the conversion gives:

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

Hence, the value of:

$\sin (90-\theta)=\dfrac{11}{15}$

Answer 2

$11/15=0.7333$
$cos^{-1}(0.7333) =42.83342$
$sin(90-47.166572) = 0.7333$

first, find the numeric value for 11/15
second to find theta, simply do the inverse cos (which is cos^-1) of the first answer.
now you know theta, just do the sin of 90 - theta and that's it!

since you know whatr cos(theta) is, you just take the inverse cos of that number to get theta and 'reverse' cos, essentially. you are just solving for theta, by reversing the cos function with cos^-1
please mark as brainliest!