1Write the following in terms of sin and cos then simplify

1.Write the following in terms of sin and cos ; then simplify if possible. (Leave your answer in terms of sin and/or cos .)

csc cot cos

2.Add or subtract as indicated. Then simplify your answer if possible. Leave your answer in terms of sin and/or cos .

sin + 1/ cos

3.Simplify the expression  as much as possible after substituting tan for x. (Assume 0° < < 90°.)

4.Simplify the expression  as much as possible after substituting 4 sin for x. (Assume 0° < < 90°.)

5.The following problem refers to right triangle ABC with C = 90°. Use the given information to find the six trigonometric functions of A.

a = 2, b = 1

6.In the following right triangle, find sin A, cos A, tan A, and sin B, cos B, tan B.

7.In the following right triangle, find sin A, cos A, tan A, and sin B, cos B, tan B.

tan (90° x°) = cot

9.Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression.

3 sin² 30° + 3 cos² 30°

10.Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression.

3(sin² 45° 2 sin 45° cos 45° + cos² 45°)

11.Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression.

(tan 45° + tan 60°)²

12.For the expression that follows, replace x with 30° and then simplify as much as possible.

2 cos(3x 45°)

13.For the expression that follows, replace z with 90° and then simplify as much as possible.

10 cos(z 30°)

x2 + 1

Solution

1.Write the following in terms of sin and cos ; then simplify if possible. (Leave your answer in terms of sin and/or cos .)

csc cot cos

= 1/sin - (cos/sin)cos

= 1/sin - cos^2/sin

= (1 - cos^2)/sin

= sin^2/sin

= sin

2.Add or subtract as indicated. Then simplify your answer if possible. Leave your answer in terms of sin and/or cos .

sin + 1/ cos

(sin*cos +1)/cos

3. x =tan

sqrt(1 +x^2) = sqrt(1 + tan^2) = sqrt(sec^2) = sec = 1/cos

4. x= 4sin

sqrt( 16 - x^2)

sqrt( 16 - 16sin^2)

sqrt(16(1-sin^2))

= 4sqrtcos^2

4cos

5) a = 2 , b =1

c is the hypotenuse as Angle C =90

So, c = sqrt(a^2 +b^2) = sqrt(4+1) = sqrt5

So,sin = a/c = 2/sqrt5 ; cos = 1/sqrt5

tan = a/b =2/1 = 2

sec = 1/cos = sqrt5

csc = 1/sin = sqrt5/2

cot = 1/tan = 1/2