Question

Find the exact values of the six trigonometric functions of the angle. sin 1665°=cos1665°=tan 1665°=

Answer 1

The functions sin(x), cos(x) and tan(x) are periodic functions.

The value for these functions are:

`\sin (1665)=-0.70710678.=-\frac{1}{\sqrt[]{2}}`
`\cos (1665)=-0.70710678\ldots=-\frac{1}{\sqrt[]{2}}`
`\tan (1665)=(\sin (1665))/(\cos (1665))=1`
`\sin (1665)=\cos (1665)=-\frac{1}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=-\frac{\sqrt[]{2}}{2}`

Rationalizing the results, we have the previous values for sin (1665) and

cos(1665) = -sqrt(2)/2.

The value for tan(1665) = 1.