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# Secant, Cosecant, and Cotangent Study Guide (page 2)

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#### Example 1

If cot(x) = , then what is csc(x)?

1 + cot2(x) = csc2(x)
A more general technique for solving such problems was introduced in Lesson 7:
• Draw a right triangle with angle x.
• Use the known trigonometric value to assign lengths to two sides of the triangle.
• Use the Pythagorean theorem to find the third side.
• Use the triangle to find all the other trigonometric values.

#### Example 2

If cot(x) = ,then what are the other five trigonometric values of x?

Draw a right triangle with angle x. If the side adjacent to angle x is A = 5 and the side opposite is O = 2 then this will ensure that cot(x) .See Figure 8.6.

The hypotenuse H is found with the Pythagorean theorem:

22 + 52 = H2
H= √29

#### Example 3

If cos(x) = , then what is csc(x)?

The angle x in Figure 8.7 has cos(x) = 0. The side O opposite x is found with the Pythagorean theorem:

(√7)2 + O2 = 52
O= √18 = 3√2

Thus, csc(x) =

Practice problems for this study guide can be found at:

Secant, Cosecant, and Cotangent Practice Questions

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