Section/Topic 5.1 Fundamental Identities

CC High School Functions

Trigonometric Functions: Prove and apply trigonometric identities

Objective Students will be able to prove trigonometric identities

Homework P191 (5-10, 15-22)

Trig Game PlanDate: 11/15/13

Fundamental Identities

Reciprocal Identities

Quotient Identities

Fundamental Identities

Pythagorean Identities

Negative-Angle Identities

Note

In trigonometric identities, θ can be an angle in degrees, an angle in radians, a real number, or a variable.

If and θ is in quadrant II, find each function

value.

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

(a) sec θ

In quadrant II, sec θ is negative, so

Pythagorean identity

Example 1:We Do

(b) sin θ

from part (a)

Quotient identity

Reciprocal identity

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

Example 1:We Do

(c) cot(– θ) Reciprocal identity

Negative-angle identity

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

Example 1:We Do

_

If and is in quadrant IV, find each function value.

(a)

In quadrant IV, is negative.

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

Example 2:You Do 2gether

If and is in quadrant IV, find each function value.

(b)

(c)

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

Example 2:You Do 2gether

FINDING TRIGONOMETRIC FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT

Example 3:You Do 2gether

Caution

To avoid a common error, when taking the square root, be sure to choose the sign based on the quadrant of θ and the function being evaluated.

Speed Test

• Reciprocal Identities (6)• Quotient identities (2)• Pythagorean identities (3)• Cofunction identities (6)