Question

which if the following is the value of sin 90°
a)r b)0 c)1/2 d)1​

Answer 1

Answer:

Let us now calculate the value of sin 90°. Consider the unit circle. That is the circle with radius 1 unit and its centre placed in origin.

sin 90 degrees

From the basic knowledge of trigonometry, we conclude that for the given right-angled triangle, the base measuring ‘x’ units and the perpendicular measuring ‘y’ units.

We know that,

For any right-angled triangle measuring with any of the angles, sine functions equal to the ratio of the length of the opposite side to the length of the hypotenuse side. So, from the figure

sinθ = y/1

Start measuring the angles from the first quadrant and end up with 90° when it reaches the positive y-axis. Now the value of y becomes 1 since it touches the circumference of the circle. Therefore the value of y becomes 1.

sinθ = y/1 = 1/1

Therefore, sin 90 degree equals to the fractional value of 1/ 1.

Sin 90° = 1

The most common trigonometric sine functions are

Sin 90 degree plus theta

sin(90∘+θ)=cosθ

Sin 90 degree minus theta

sin(90∘−θ)=cosθ

Some other trigonometric sine identities are as follows:

sinx=1cscx

sin2x+cos2x=1

sin(−x)=−sinx

Sin 2x = 2 sin x cos x

In the same way, we can derive other values of sin angles like 0°, 30°,45°,60°,90°,180°,270° and 360°. Below is the trigonometry table, which defines all the values of sine along with other trigonometric ratios.