Question

Write the expression as the sine cosine or tangent of an angle calculator.

Answer 1

The student's question pertains to expressing mathematical functions as the sine, cosine, or tangent of an angle, which are basic trigonometric functions involving the ratios of sides in a right triangle. These functions and their related identities are essential in solving various problems in trigonometry and understanding oscillations in wave functions.

Step-by-step explanation:

The question revolves around the concept of expressing mathematical functions as the sine, cosine, or tangent of an angle—a fundamental principle in trigonometry. When you have the measurements of the sides of a right triangle, you can define these trigonometric ratios.

For any angle A in a right triangle, cosine (cos) represents the ratio of the adjacent side to the hypotenuse, which is expressed as Ax/A. Similarly, the sine (sin) is the ratio of the opposite side to the hypotenuse, denoted as Ay/A. For the tangent (tan), it is the ratio of the opposite side to the adjacent side, which you can find using tan(A) = y/x. These ratios help form the basis for solving problems involving right-angled triangles and can also extend, through certain mathematical relationships, into more complicated wave functions as in the case of sine and cosine functions representing oscillations.

In trigonometry, there are also several important identities, like the sine of double angles, expressed as sin(2A) = 2sinAcosA, and the cosine of double angles, such as cos(2A) = cos2A - sin2A. There are also identities that relate the sines and cosines of two angles to each other, such as sina + sinb = 2 sin((a + b)/2) cos((a - b)/2).

Answer 2

hello your question is incomplete here is the complete question

write the expression as the sine, cosine, or tangent of an angle.

`sin 60 cos 15 + cos 60 sin 15`

answer :
`sin 60 cos 15 + cos 60 sin 15 = sin 75`

Step-by-step explanation:

To write the expression as the sine,cosine or tangent of an angle we will employ the trigonometry identity

`sin 60 cos 15 + cos 60 sin 15` can be represented in the form of ;

sin( u + v ) = sin u cos v + cos u sin v --------- (1)

comparing equation 1 with the given expression

u = 60 and v = 15

therefore writing the expression in the form of the sine of an angle would be the answer

= sin( 60 + 15 ) = sin 60 cos 15 + cos 60 sin 15

hence sin ( 75 ) = sin 60 cos 15 + cos 60 sin 15