7 5 the other trigonometric functions
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7.5 The Other Trigonometric Functions. 7.5 The Other Trig Functions. Objectives: Evaluate csc , sec and cot Vocabulary: Cosecant, Secant, Cotangent. Right Triangle Trig. Functions. Let  be an acute angle of a right triangle. 7.5 The Other Trig Functions.

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7.5 The Other Trigonometric Functions

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7 5 the other trigonometric functions

7.5 The Other Trigonometric Functions


7 5 the other trigonometric functions

7.5 The Other Trig Functions

Objectives:

Evaluate csc, sec and cot

Vocabulary: Cosecant, Secant, Cotangent


Right triangle trig functions

Right Triangle Trig. Functions

Let  be an acute angle of a right triangle.


If is a second quadrant angle and sin is 3 5 find the remaining five functions

7.5 The Other Trig Functions

If is a second quadrant angle and sin is 3/5, find the remaining five functions.


Find the six trig functions for 330

7.5 The Other Trig Functions

Find the six trig functions for: 330°


7 5 the other trigonometric functions

A

S

30o

330o

x

T

C

Find the six trig functions of 330o .

[Solution] First draw the 330o angle.

Second, find the reference angle, 360o– 330o= 30o

To compute the trig functions of the 30o angle, draw the “special” triangle or recall from the table.

Determine the correct sign for the trig functions of 330o . Only the cosine and the secant are “+”.


7 5 the other trigonometric functions

Find the six trig functions of 330o .

[Solution] The six trig functions of 330o are:


Find the six trig functions for

7.5 The Other Trig Functions

Find the six trig functions for:


7 5 the other trigonometric functions

Find the six trig functions of .

Before we write the functions, we need to determine the signs for each function. Remember “All Students Take Calculus”. Since the angle, , is located in the 3rd quadrant, only the tangent and cotangent are positive. All the other functions are negative..

y

A

S

x

T

C


Find the six trig functions for1

7.5 The Other Trig Functions

Find the six trig functions for:


7 5 the other trigonometric functions

We see that the angle is located in the 3rd quadrant.

0 radians

We know that is the same as 45 , so the reference angle is 45 . Using the special triangle.

A

Note that the reference angle is .

S

T

C

Find the six trig functions for .

We will first draw the angle to determine the quadrant.


Tb p 286 13 27 odd skip 19 21

7.5 The Other Trig Functions

TB p. 286#13-27 odd skip 19 & 21


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