Derive and Use Trigonometric Identities
Read this topicExplanations 8
- Trigonometric Identities, or Trig Identities for short, are equalities that relate the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Let'…
By Cindy Zhang, Moor Xu, Jonathan Heller, Anusha Rahman
- Sometimes, where working with a trigonometric expression, it is useful to replace all the sinθ\sin \thetasinθ and cosθ\cos\thetacosθ with a rational expression in terms of a s…
By David Stoner
- Complex Numbers in Proving Trig Identities\large{\textbf{Complex Numbers in Proving Trig Identities}}Complex Numbers in Proving Trig Identities Basic Facts\large{\textbf{Basic F…
By Jubayer Nirjhor, Andrew Machkasov, Joshua Siktar, Anusha Rahman
- Trigonometric Identities There are many trigonometric identities in the world, and I'm not going to list them all here. However, I'll continue with some of the most common and i…
By Zi Song Yeoh, Chong Jing Quan, Alex Federspiel, Anusha Rahman
- Some of us have seen the formula eiθ=cosθ+isinθe^{i \theta} = \cos \theta + i \sin \thetaeiθ=cosθ+isinθ before (if you haven't, check it out here!). However, this doesn't real…
By Vincent Huang, Kevin Chang, Rajiv Movva, Victor Wang
- In this explanation we're going to prove the identity tan(2x)=2sin(x)2cos(x)−sec(x).\tan(2x) = \frac{2\sin(x)}{2\cos(x) - \sec(x)}.tan(2x)=2cos(x)−sec(x)2sin(x). In doing s…
By Joshua Siktar, Joshua Siktar
- Verifying Trigonometric Identities by Professor Dave Explains In this video by Professor Dave Explains, you will be able to prove and verify the trigonometric identities.
By Anusha Rahman
- Creating New Trig Identities from Old Ones Trig identities are math rules that are always true for certain angle functions like sine, cosine, and tangent. We've already learned …
By Anusha Rahman
Problems 23
- What is the amplitude of sin(x)+cos(x)\sin(x) + \cos(x)sin(x)+cos(x)?
- Simplify csc(t)tan(t)\csc(t)\tan(t)csc(t)tan(t) to an expression involving a single trig function with no fractions.
- Simplify cos(t)csc(t)\cos(t)\csc(t)cos(t)csc(t) to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify sec(t)−cos(t)sin(t)\frac{\sec(t)-\cos(t)}{\sin(t)}sin(t)sec(t)−cos(t) to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify 1+sin(t)1+csc(t)\frac{1+\sin(t)}{1+\csc(t)}1+csc(t)1+sin(t) to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify, , to an expression involving a single trig function with no fractions.
- Simplify sin2x+cos2x−csc2x\sin^2x+\cos^2x-\csc^2xsin2x+cos2x−csc2x
- Select all expressions below that are equivalent to sec2x+csc2xcsc2xsec2x.\frac{\sec^2x+\csc^2x}{\csc^2x\sec^2x}.csc2xsec2xsec2x+csc2x.
- Simplify 4cscxsinx=cos2x4\csc x\sin x=\cos^2x4cscxsinx=cos2x
- Verify 1sec2x=1−1csc2x\frac{1}{\sec^2x}=1-\frac{1}{\csc^2x}sec2x1=1−csc2x1
- Verify csc(x)\csc(x)csc(x) - cot(x)\cot(x)cot(x) = 1csc(x)+cot(x)\frac{1}{csc(x) + cot(x)}csc(x)+cot(x)1.
- Simplify sec(x)sin(x)cotx\frac{\sec(x)\sin(x)}{\cot x}cotxsec(x)sin(x).
- Simplify sin2(x)cot(x)cos(x)−1tan(x)\frac{sin^2(x)cot(x)}{cos(x)-\frac{1}{tan(x)}}cos(x)−tan(x)1sin2(x)cot(x).
- Simplify sec2(x)+2tan(x)tan2(x)+tan(x)\frac{sec^2(x)+2tan(x)}{tan^2(x)+tan(x)}tan2(x)+tan(x)sec2(x)+2tan(x).
- Simplify until you reach a single trig function: 2tanasin2a+cos2a+sec2a−1\frac{2\tan a}{\sin ^{2}a +\cos^{2}a +\sec^{2}a -1}sin2a+cos2a+sec2a−12tana
- Simplify: sin2a+cot2a+1csc2a−cos2a+1\frac {\sin^{2}a+\cot^{2}a+1}{\csc^{2}a-\cos^{2}a+1}csc2a−cos2a+1sin2a+cot2a+1
- Simplify: csc2a+1−cot2asec2a−tan2a\frac {\csc^{2}a+1-\cot^{2}a}{\sec^{2}a-\tan^{2}a}sec2a−tan2acsc2a+1−cot2a
- Simplify: sin4x−cos4x\sin^{4}x - \cos^{4}xsin4x−cos4x