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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)