Question

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1)HOW TO FIND TRIGNOMETRIC RATIOS MORE THAN 90 .LIKE SIN 270

2)HOW TO FIND TRIGNOMETRIC RATIOS LIKE SIN37...

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Answer 1

it's easy.

1)after 90 the trigonometric ratios are repeated in a reverse order and after 180 the whole cycle from 0 to 180 is repeated once again

2) there is not a specific method to find rarios like sin37 but the value of sin 37 and 53 is 3/5 and 4/5 respectively.

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Answer 2

There are two possible definitions of the trigonometric ratios:

The trigonometric ratios can be defined for angles greater than 0∘ and less than 90∘ using right triangles. In particular, sin(θ) is defined as the ratio of the lengths of the opposite leg and the hypotenuse, and cos(θ) is defined as the ratio of the lengths of the adjacent leg and the hypotenuse.

The trigonometric ratios can be defined for any angle using the unit circle. In this definition, sin(θ) is the y-coordinate of a point on the unit circle with angle θ, and cos(θ) is the x-coordinate of a point on the unit circle with angle θ.

The unit circle definition is the same as the triangle definition for angles between 0 and 90∘, but is more general since it works for any angle. The following picture from Wikipedia illustrates this definition:

(Fig.1)

For each point, the x-coordinate is the cosine, and the y-coordinate is the sine.

This picture only shows angles between 0∘ and 360∘, but you can extend to less than 0∘ by continuing clockwise around the circle, or to greater than 360∘ by continuing counterclockwise.

The following pictures show graphs of sin(x) and cos(x) for −2π≤x≤2π. (The x-axis is the angle measured in radians.)

(Fig.2)