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Warm-Up. If (2, -5) is on the terminal side of an angle α in standard position, find the 6 trig functions. If cos α <0 and cot >0, in what quadrant does α terminate? If cos α = 4/5 and α is in quadrant IV, find the values of cosecant and secant. . Trig Game Plan Date: 9/23/13.

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warm up
Warm-Up
  • If (2, -5) is on the terminal side of an angle α in standard position, find the 6 trig functions.
  • If cos α <0 and cot >0, in what quadrant does α terminate?
  • If cos α = 4/5 and α is in quadrant IV, find the values of cosecant and secant.
slide3

Right-Triangle-Based Definitions of Trigonometric Functions

For any acute angle A in standard position,

slide4

Right-Triangle-Based Definitions

of Trigonometric Functions (page 62)

For any acute angle A in standard position,

slide5

FINDING TRIGONOMETRIC FUNCTION VALUES OF AN ACUTE ANGLE

Example 1

Find the sine, cosine, and tangent values for angles A and B.

slide6

FINDING TRIGONOMETRIC FUNCTION VALUES OF AN ACUTE ANGLE (cont.)

Example 1

Find the sine, cosine, and tangent values for angles A and B.

slide7

CofunctionIdentities (page 63)

For any acute angle A in standard position,

sin A = cos(90  A) cscA = sec(90  A)

tan A = cot(90  A) cosA = sin(90  A)

sec A = csc(90  A) cot A = tan(90  A)

slide8

WRITING FUNCTIONS IN TERMS OF COFUNCTIONS

Example 2a

Write each function in terms of its cofunction.

(a) cos 52°

= sin (90° – 52°) = sin 38°

(b) tan 71°

= cot (90° – 71°) = cot 19°

(c) sec 24°

= csc (90° – 24°) = csc 66°

slide9

WRITING FUNCTIONS IN TERMS OF COFUNCTIONS

Example 2b

  • Write each function in terms of its cofunction.

(a) sin 9°

= cos (90° – 9°) = cos 81°

(b) cot 76°

= tan (90° – 76°) = tan 14°

(c) csc 45°

= sec (90° – 45°) = sec 45°

slide10

SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES

Example 3a

Find one solution for the equation. Assume all angles involved are acute angles.

(a)

Fsin(θ+4)=cos(3θ+2)

Since sine and cosine are cofunctions, the equation is true if the sum of the angles is 90º.

Combine terms.

Subtract 6°.

Divide by 4.

slide11

SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES (continued)

Example 3a

Find one solution for the equation. Assume all angles involved are acute angles.

(b)

Ftan(2θ-18)=cot(θ+18)

Since tangent and cotangent are cofunctions, the equation is true if the sum of the angles is 90º.

slide12

Example 3b

  • Find one solution for the equation. Assume all angles involved are acute angles.

(a)

Since cotangent and tangent are cofunctions, the equation is true if the sum of the angles is 90º.

slide13

Example 3b

  • Find one solution for the equation. Assume all angles involved are acute angles.

(b)

Since secant and cosecant are cofunctions, the equation is true if the sum of the angles is 90º.

re cap
Re-Cap

Write all 17 identities

  • Reciprocal (6)
  • Pythagoreans (3)
  • Quotients (2)
  • Cofunctions(6)

Memorization Quiz

tomorrow after warm up