sprecalc7-6-2-002-1

1.

SPreCalc7 6.2.001.

A right triangle with an angle θ is shown in the figure.

(a) Label the “opposite” and “adjacent” sides of θ and the hypotenuse of the triangle.
a:

b:

c:

(b) The trigonometric functions of the angle θ are defined as follows.

sin(θ) =

cos(θ) =

tan(θ) =

(c) The trigonometric ratios do not depend on the size of the triangle. This is because all right triangles with the same acute angle θ are .

2.

SPreCalc7 6.2.002.

The reciprocal identities state thatcsc(θ) =

 1 —Select—sin(θ)cos(θ)tan(θ)

sec(θ) =

 1 —Select—sin(θ)cos(θ)tan(θ)

cot(θ) =

 1 —Select—sin(θ)cos(θ)tan(θ)

.

3.

SPreCalc7 6.2.006.

Find the exact values of the six trigonometric ratios of the angle θ in the triangle.

 sin(θ) = cos(θ) = tan(θ) = csc(θ) = sec(θ) = cot(θ) =

4.

SPreCalc7 6.2.008.

Find the exact values of the six trigonometric ratios of the angle θ in the triangle.

 sin(θ) = cos(θ) = tan(θ) = csc(θ) = sec(θ) = cot(θ) =

5.

SPreCalc7 6.2.009.

Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β).

(a)sin(α) and cos(β)

(b)tan(α) and cot(β)

(c)sec(α) and csc(β)

6.

SPreCalc7 6.2.013.

Use a calculator to evaluate the expression. Round your answer to five decimal places.(a)sec(17°)

(b)

tan(54°)

7.

SPreCalc7 6.2.017.

Find the side labeled x.
x =

 7

8.

SPreCalc7 6.2.020.

Find the side labeled x. State your answer rounded to 5 decimal places.
x =

 57° 21

9.

SPreCalc7 6.2.022.

Express x and y in terms of trigonometric ratios of θ. (Express your answer in terms of θ only.)

 x = y =

10.

SPreCalc7 6.2.024.MI.

Sketch a triangle that has acute angle θ.cos(θ) =

 4 5

Find the other five trigonometric ratios of θ.

 sin(θ) = tan(θ) = csc(θ) = sec(θ) = cot(θ) =

11.

SPreCalc7 6.2.025.

Sketch a triangle that has acute angle θ.cot(θ) = 2

Find the other five trigonometric ratios of θ.

 sin(θ) = cos(θ) = tan(θ) = csc(θ) = sec(θ) =

12.

SPreCalc7 6.2.026.

Sketch a triangle that has acute angle θ.tan(θ) =

 3

Find the other five trigonometric ratios of θ.

 sin(θ) = cos(θ) = csc(θ) = sec(θ) = cot(θ) =

13.

SPreCalc7 6.2.029.

Evaluate the expression without using a calculator.sin

 π 6

+ cos

 π 6

14.

SPreCalc7 6.2.032.

Evaluate the expression without using a calculator.(sin 60°)2 + (cos 60°)2

15.

SPreCalc7 6.2.038.MI.

Solve the right triangle.

 140

Find the length of the side adjacent to the given angle. (Round your answer to two decimal places.)

Find the length of the hypotenuse. (Round your answer to two decimal places.)

Find the other acute angle.

°

16.

SPreCalc7 6.2.041.

Solve the right triangle.

 42.5

Find the length of the side opposite to the given angle. (Round your answer to two decimal places.)

Find the length of the side adjacent to the given angle. (Round your answer to two decimal places.)

Find the other acute angle.

17.

SPreCalc7 6.2.047.

Find x rounded to one decimal place.
x =

 130

18.

SPreCalc7 6.2.053.

The angle of elevation to the top of a very tall Building is found to be 8° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building. (Round your answer to the nearest foot.)
ft

Is this the question you were looking for? Place your Order Here