Question

Explain why the sines and cosines values cannot be greater than 1. (consider it for a right-angled triangle).

Answer 1

Answer:

1=1 Classic Pythagorean theorem. The value of the sin cannot be more than 1 because the triangle that the trig functions are based on no longer exists

Answer 2

If the value of the sin is 1 or greater the leg of the triangle is the same as the hypothenuse and there is only a line not a triangle.

Explanation:

The trig functions are based on the Pythagorean Theorem

A2+B2=C2

sin=A

cos=B

hyp=C

so

sin2+cos2=hyp2

In the classic unit trig triangle the Hypothenuse is 1 so

sin2+cos2=12

This can be illustrated by a 45 degree right triangle

sin=cos so

sin45=0.707

cos45=0.707

0.7072+0.7072=12

0.5+0.5=1

1=1 Classic Pythagorean theorem.

Now if the value of the sin is 1 the value of the cos must be 0

12+02=12

1=1

So if the angles of the triangle are such that sin=1andcos=0there is no longer a triangle but just a vertical line because the line adjacent is 0

The value of the sin cannot be more than 1 because the triangle that the trig functions are based on no longer exists.