What is the value of sine of θ
when θ=90°
?(1 point)
Responses
-1
-1
12
1 half
0
0
1
To find the value of sine of θ when θ is 90°, you can use the unit circle or trigonometric identities.
Option 1: Using the Unit Circle
- Draw a unit circle (a circle with a radius of 1 unit).
- Mark the point where the angle θ = 90° intersects the unit circle.
- The y-coordinate of this point is equal to the sine of θ.
- In this case, when θ is 90°, the y-coordinate is 1.
- Therefore, the value of sine of θ when θ is 90° is 1.
Option 2: Using Trigonometric Identities
- The sine of θ is defined as the ratio of the length of the side opposite θ to the length of the hypotenuse in a right triangle.
- In a right triangle, if one of the angles is 90°, then the side opposite that angle is the longest side (the hypotenuse).
- So, when θ is 90°, the side opposite θ is equal to the hypotenuse.
- Therefore, the sine of θ when θ is 90° is equal to the ratio of the hypotenuse to itself, which is 1.
In both cases, the value of sine of θ when θ is 90° is 1.