Question

What angle has the same sine value between 0-180? as Sin 24

A Sine 156
B Sine 123
C Sine 145
D Sine 154

Answer 1

OPTION A.

The angle with the same sine value as sin 24 degrees between 0 and 180 degrees is 156 degrees because the sine function is symmetrical around 90 degrees in the first and second quadrants.

Step-by-step explanation:

The student is asking about sine values of angles in degrees. Specifically, which angle between 0 and 180 degrees has the same sine value as sin 24 degrees. To find an angle with the same sine value in the range given (0-180 degrees), one must consider the symmetry of the sine function in the first and second quadrants. In the first quadrant (0 to 90 degrees), sine values are positive and increase up to 1. In the second quadrant (90 to 180 degrees), sine values are still positive but decrease back down to 0.

Since 24 degrees is in the first quadrant, we want to find the equivalent angle in the second quadrant. The related angle in the second quadrant that will have the same sine value is found by subtracting the given angle from 180 degrees. This is because the sine function is symmetrical about 90 degrees.

Therefore, the equivalent angle will be 180 - 24 = 156 degrees. This means sin 156 degrees will have the same value as sin 24 degrees.

Answer 2

`Sin156`

Step-by-step explanation:

Given

`Sin24`

Required

Find equivalent between 0 to 180;

Let 24 be represented by
`\theta`

So,
`\theta = 24`

From Trigonometry ratios;

`Sin\theta = Sin(180 - \theta)` where
`0\leq \theta \leq 180`

Recall that
`\theta = 24`

So, we have to substitute 24 for
`\theta` in the above expression.

This gives

`Sin24= Sin(180 - 24)`

Subtract 24 from 180

`Sin24= Sin156`

Hence, the equivalent of
`Sin24` is
`Sin156`