sec(x) = 1/cos(x)You are given tan(x) = 3 and cos(x)> 0Note:1st Quadrant : sin(x) > 0, cos(x) > 0, and tan(x) > 02nd Quadrant: sin(x) < 0, cos(x) > 0, and tan(x) < 03rd Quadrant: sin(x) > 0, cos(x) < 0, and tan(x) < 04th Quadrant: sin(x) <...
sec θ±1/cos θ cosec θ±1/√(1-cos2θ) Cos Calculus For cosine functionf(x)=cos(x), the derivative and the integral will be given as: Derivative of cos(x), f′ (x) = −sin (x) Integral of cos(x), ∫f (x) dx = sin(x) + C) [where C is the constant of integra...
C(x)cosxtanx=C(x)sinx⟹C′(x)cosx=secx⟹C′(x)=sec2xSoC(x)=tanx+k This gives a general solution of y=sinx+kcosx. Substituting in to the original equation: cosx−ksinx+cosxsin2(x)+ksinx=secxcosxcos2x+sin2x=secx ... More Items Share Copy Copied to clipboard Examples ...
Draw the graph ofy=cosxin[−π,2π]. View Solution Draw the graph ofy=cos2x. View Solution Draw the graph ofy=cos−1(x2). View Solution Draw the graph ofy=−cos−1(cosx). View Solution Draw the graph ofy=cos−1x3and compare with the graph ofy=cos−1x. ...
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Example b= 3" c= 5" cosα=b/c= 3 / 5 = 0.6 Graph of cosine TBD Cosine rules Rule nameRule Symmetrycos(-θ) = cosθ Symmetrycos(90°-θ) = sinθ Pythagorean identitysin2(α) + cos2(α) = 1 cosθ= sinθ/ tanθ cosθ= 1 / secθ ...
What is the derivative of sin(x) and cos(x)? The derivative of cos(x) is -sin(x). The derivative of sin(x) is cos(x). Both derivatives can be derived using Euler's complex representation of sine and cosine or by rewriting sin(x) as 1/csc(x) and cos(x) as 1/sec(x).What...
C(x)cosxtanx=C(x)sinx⟹C′(x)cosx=secx⟹C′(x)=sec2xSoC(x)=tanx+kThis gives a general solution ofy=sinx+kcosx. Substituting in to the original equation:cosx−ksinx+cosxsin2(x)+ksinx=secxcosxcos2x+sin2x=secx... ...
Secant, on the other hand, is a separate trigonometric function that is the reciprocal of the cosine value. The following formulas show the relationship between cosine andsecant. cos(α) =adjacent/hypotenuse=b/c sec(α) =hypotenuse/adjacent=c/b=1/cos(α) ...
are always positive. To be accurate the value of cos 360 is 1. The function oftrigonometrythat relates an angle of the right-angled triangle to the ratio of sides is termed a trigonometric function. There are 6 trigonometric functions, sine, cosine, tangent, cotangent, secant, and cosecant....