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
tan x =
cot x =
These reciprocals are used to find the value of trig functions:
sin x = ; cosec x =
cos x = ; sec x =
tan x = ; cot x =
- 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
+
= 1
+ 1 =
1 + =
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 67° + cos 65° 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 =
2. tan θ = 9/5
3. cos 23° + sin 25°
4. sec θ = 10/7
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