Why does tan equal to sin/cos? - Socratic
WEBJim H. Apr 15, 2015. The best answer to this question depends on the definitions you're using for the trigonometric functions: Unit circle: t correspond to point (x,y) on the circle x2 + y2 = 1. Define: sint = y, , cost = x, , tant = y x. The result is immediate. Point (x,y) on the terminal side of t and r = √x2 + y2.
How do you simplify cosx/sinx? - Socratic
WEBMay 27, 2016 · cot(x) cos(x)/sin(x) = cot(x) How do you apply the fundamental identities to values of #theta# and show that they are true?
Proving Identities - Trigonometry - Socratic
WEBThe Trigonometric Identities are equations that are true for Right Angled Triangles. Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.
How do you simplify sin theta / (1+ cos theta) + (1+cos ... - Socratic
WEBJun 2, 2016 · Using the pythagorean identity cos2θ + sin2θ = 1. = 2 + 2cosθ sinθ ×(1 +cosθ) = 2(1 + cosθ) sinθ ×(1 +cosθ) = 2 sinθ. Now recall that 1 sinθ = cscθ. = 2cscθ. Hopefully this helps! Start by putting on a common denominator. (sin theta xx sin theta)/ ( (1 + costheta) xx sin theta) + ( (1 + costheta) xx (1+ costheta))/ (sin theta xx ...
Fundamental Identities - Trigonometry - Socratic
WEBHere are a few examples I have prepared: a) Simplify: tanx/cscx xx secx. Apply the quotient identity tantheta = sintheta/costheta and the reciprocal identities csctheta = 1/sintheta and sectheta = 1/costheta. = (sinx/cosx)/ (1/sinx) xx 1/cosx. =sinx/cosx xx …
Simplify #sin theta / (1+cos theta)# - Socratic
WEBJun 25, 2017 · sinθ 1 + cosθ = cscθ − cotθ. Explanation: I'm not sure what you are wanting, but here's one way to simplify the expression: sinθ 1 + cosθ = sinθ(1 − cosθ) (1 +cosθ)(1 − cosθ) sinθ 1 + cosθ = sinθ(1 − cosθ) 1 − cos2θ. sinθ 1 + cosθ = sinθ(1 − cosθ) sin2θ. sinθ 1 + cosθ = 1 − cosθ sinθ. sinθ 1 + cosθ = 1 ...
How do you solve sin 2theta sin theta = cos theta? | Socratic
WEBMay 16, 2015 · 1 − cos2θ = 1 2. So cos2θ = 1 2 and cosθ = ± 1 √2. This is true for. θ = π 4 + nπ 2 for all n in Z. From the formula for sin (2theta) we have sin 2theta = 2sin theta cos theta From Pythagoras theorem we have sin^2 theta + cos^2 theta = 1 So sin 2theta sin theta = (2sin theta cos theta)sin theta = 2sin^2 theta cos theta =2 (1-cos^2 ...
How do you simplify #Sin(Cos^-1 x)#? - Socratic
WEBMay 9, 2016 · The Pythagorean theorem then allows us to solve for the second leg as √1 −x2. With this, we can now find sin(cos−1(x)) as the quotient of the opposite leg and the hypotenuse. sin(cos−1(x)) = sin(a) = √1 −x2 1 = √1 − x2. sin (cos^ (-1) (x)) = sqrt (1-x^2) Let's draw a right triangle with an angle of a = cos^ (-1) (x).
How do you simplify #sin(-x)/cos(-x)#? - Socratic
WEBJan 13, 2017 · Explanation: Because it is an even function, cos(−x) = cos(x) Similarly, because it is an odd function, #sin (-x)=-sin (x) So, the above ratio can be written. − sin(x) cos(x) which is equal to −tan(x) -tanx cosx is an even function. This means that cos (-x)=cosx sinx is an odd function. This means that sin (-x)=-sinx sin (-x)/cos (-x ...
Sin^8(75°)-cos^8(75°) - Socratic
WEBOct 21, 2017 · #Sin^8(75°)-cos^8(75°)# #(Sin^4(75°)-cos^4(75°))(Sin^4(75°)+cos^4(75°)# #=(Sin^2(75°)+cos^2(75°)) (Sin^2(75°)-cos^2(75°))(Sin^4(75°)+cos^4(75°)#