Online Trigonometry Tutoring: Trigonometric Identities
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Learn Trigonometric Identities from certified Online Trigonometry tutor:
Identity is an equation which is always true for all defined values
Tangent and cotangent functions can be expressed in terms of the sine and cosine functions
These reciprocals are used to find the value of trig functions:
- Pythagorean Identities is to help simplify trigonometric expressions.
- Simplifying trigonometric expressions to create a factorable expression used to find missing trigonometric values.
- Used to find missing trigonometric values
Example 1
- Prove that tan y/sin y = sec y
Expressing it in terms of sin y or cos y, we get
LHS = tan y × 1/sin y
= (sin y/cos y) × 1/sin y (tan A = sin A/cos A)
= 1/cos y
= sec y                (since 1/cos A = sec A)
= RHS
Example 2
Verify the identities
1/sec2a = sin2a . cos2a + cos4a
RHS = cos2a (sin2a + cos2a)
= cos2a (1) {we know, sin2a + cos2a =1}
= cos2a
LHS = 1/sec2a = 1/(1/ cos2a) = cos2a
Check Point
Problem 1. If sinθ = 2/3, find cosθ.
Problem 2. If cos θ = 5/11 and sin θ = 9/11, what is the value of tan θ?
Problem 3. Express sin 670 + cos 650 in terms of trigonometric ratios of angle between 0 and 45 degrees.
Problem 4. If cos θ = .7, find the value of sec θ.
Answers:
1. cos θ = 5/3
2. tan θ = 9/5
3. cos 230 + sin 250
4. sec θ = 10/7
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