What is cos(θ-90)? - Socratic
WEBJun 17, 2018 — 1 Answer. using the addition formula for cos. ∙ xcos(x −y) = cosxcosy + sinxsiny. cos(θ − 90) = cosθcos90 + sinθsin90. = cosθ(0) +sinθ(1) = sinθ.
Express $\cos 6\theta - Mathematics Stack Exchange
WEBSince $$\cos 2a =2\cos ^{2}a -1, \qquad\sin 2a =2\sin a\cos a,$$ $$\cos (a+b)=\cos a\cos b-\sin a\sin b,$$ and $$ \begin{eqnarray*} \cos 3\theta &=&\cos (2\theta ...
Double Angle Identities - Trigonometry - Socratic
WEBAnswer: As below. Explanation: Following table gives the double angle identities which can be used while solving the equations. You can also have sin2θ,cos2θ expressed in terms of tanθ as under. sin2θ = 2tanθ 1 +tan2θ. cos2θ = 1 …
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 …
Why is cos -x equal to cos x? - Mathematics Stack Exchange
WEBApr 27, 2016 — 1. Intuitively cos(−θ) cos (− θ) measures the x x -coordinate of a vector that measures θ θ degrees below the positive x x -axis, so this is why we have cos(−θ) = cos θ cos (− θ) = cos θ. Another way of seeing this is through the series representation of …
trigonometry - Why $\cos(-\theta)$ gives positive values while in …
WEBIf $\cos(-\theta) = \cos \theta$ then why is the value of $\cos(-\theta) $ negative when $\theta \lt -90^\circ$? 1 General values of $\theta$ for which $(\sin\theta)x^2+(2\cos\theta)x+\frac{\cos\theta+\sin\theta}{2}$ is the square of a …
Integration of $d(\\cos\\theta)$ - Mathematics Stack Exchange
WEBAdd a comment. 2. Think of it as u u substitution (or the chain rule), where your u = cos(θ) u = cos (θ) so that. du = d(cos(θ)) = − sin(θ)dθ d u = d (cos (θ)) = − sin (θ) d θ. Edit: And of course by the fundamental theorem of calculus, integrating d(cos(θ) d (cos (θ) this is just cos(θ) cos (θ). Share.
What is cos(-theta) in terms of costheta? - Socratic
WEBDec 7, 2015 — This means that the two points have coordinates (x,y) and (x, −y). Since the cosine is the x -coordinate of the points on the unit circle, you see that the two points have the same cosine, and opposite sine. In fact, the cosine is an even function, which means exactly that cos(x) = cos(− x), while the sine is odd, which means that sin(x ...
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.
calculus - Why does $r = \cos \theta$ produce a circle?
WEBNov 5, 2016 — It is the other point that the equation r = cos θ r = cos θ specifies. On the vertical line, θ = π/2 + πn θ = π / 2 + π n, we have cos θ = 0 cos θ = 0, so this gives the origin. As for why this gives a circle, the other answers have given algebraic proofs for this.
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