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Write each function in terms of its cofunction .PowerPoint Presentation

Write each function in terms of its cofunction .

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Write each function in terms of its cofunction .

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WARM-UP

Write each function in terms of its cofunction.

(a)cos 48°

= sin (90° – 48°) = sin 42°

(b)tan 67°

= cot (90° – 67°) = cot 23°

(c)sec 44°

= csc (90° – 44°) = csc 46°

Write all identities

- Pythagoreans (3)
- Quotients (2)
- Cofunctions (6)
- Reciprocal (6)
Solve the quadratics

5. x2 + 11x + 24 = 0

6. (x – 3)2 – 4 = 0

7. Write the quadratic formula.

Trig Game PlanDate: 9/24/13

As A increases, y increases and x decreases.

Since r is fixed,

sin A increases

csc A decreases

cos A decreases

sec A increases

tan A increases

cot A decreases

COMPARING FUNCTION VALUES OF ACUTE ANGLES

Example 1a

Determine whether each statement is true or false.

(a) sin 21° > sin 18° (b) cos 49° ≤ cos 56°

(a)In the interval from 0 to 90, as the angle increases, so does the sine of the angle, which makes sin 21° > sin 18° a true statement.

(b)In the interval from 0 to 90, as the angle increases, the cosine of the angle decreases, which makes cos 49° ≤ cos 56° a false statement.

COMPARING FUNCTION VALUES OF ACUTE ANGLES

Example 1b

- Determine whether each statement is true or false.

(a)tan 25° < tan 23°

In the interval from 0° to 90°, as the angle increases, the tangent of the angle increases.

tan 25° < tan 23° is false.

(b)csc 44° < csc 40°

In the interval from 0° to 90°, as the angle increases, the sine of the angle increases, so the cosecant of the angle decreases.

csc 44° < csc 40° is true.

Bisect one angle of an equilateral to create two 30°-60°-90° triangles.

Use the Pythagorean theorem to solve for x.

FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60°

Example 2

Find the six trigonometric function values for a 60° angle.

FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° (continued)

Example 2

Find the six trigonometric function values for a 60° angle.

Use the Pythagorean theorem to solve for r.

adjacent

sin

cos

tan

cot

sec

csc

30

45

60