How do you simplify secx/tanx? - Socratic
2016年11月13日 · Explanation: Let's use the definitions of secx and tanx to simplify this. We know. secx = 1 cosx and tanx = sinx cosx. Let's plug these values into our original expression. we get. 1 cosx sinx cosx = 1 cosx sinx cosx ⇒ 1 sinx ⇒ cscx. Therefore, secx tanx = …
How do you solve tanx=-1? - Socratic
2016年9月12日 · Explanation: Use trig table of special arcs: When tan x = - 1 --> x = 3π 4. General answers: x = 3π 4 +kπ. Answer link.
What is the taylor series expansion for the tangent function (tanx ...
2018年5月22日 · We start with the function. f (0)(x) = f (x) = tanx. Then, we compute the first few derivatives: = sec2(x) Now we have the derivatives, we can compute their values when x = 0. Which permits us to form the Maclaurin serie: f (x) = (0) + 1 1x + 0 2 x2 + 2 6 x3 +... f (n)(0) n! xn +... = x + 1 3x3 + 2 155 x5 +...
Proving Identities - Trigonometry - Socratic
The 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.
What is the limit as x approaches 0 of tanx/x? | Socratic
2018年6月12日 · From the graph, you can see that as x → 0, tanx x approaches 1. Remember the famous limit: lim x→0 sinx x = 1. Now, let's look at our problem and manipulate it a bit: lim x→0 tanx x. = lim x→0 sinx/cosx x. = lim x→0 (sinx x) cosx. = lim x→0 (sinx x) ⋅ (1 cosx)
Fundamental Identities - Trigonometry - Socratic
Here are a few examples I have prepared: a) Simplify: tanx cscx ×secx. Apply the quotient identity tanθ = sinθ cosθ and the reciprocal identities cscθ = 1 sinθ and secθ = 1 cosθ. = sinx cosx 1 sinx × 1 cosx. = sinx cosx × sinx 1 × 1 cosx. = sin2x cos2x. Reapplying the quotient identity, in reverse form: = tan2x. b) Simplify: cscβ ...
Why does tan equal to sin/cos? - Socratic
2015年4月15日 · sinθ = opposite adjacent = opp adj. The result follow from : sinθ cosθ = opp hyp adj hyp = (opp hyp) ⋅ (hyp adj) = opp adj = tanθ. Answer link. 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 x^2+y^2 =1 Define: sint = y, , cos ...
What is the antiderivative of #tan(x)#? - Socratic
2014年10月16日 · 3 Answers. Recall: ∫ g'(x) g(x) dx = ln|g(x)| + C. (You can verify this by substitution u = g(x).) Now, let us look at the posted antiderivative. By the trig identity tanx = sinx cosx, ∫tanxdx = ∫ sinx cosx dx. by rewriting it a bit further to fit the form above, = − ∫ −sinx cosx dx.
How do you simplify #tan(x)/sec(x) - Socratic
2016年7月31日 · =sinx tanx/secx =(tanx)(cosx) =((sinx)(cosx))/cosx =sinx
How do you solve #tanx=1# and find all exact general solutions?
2018年3月2日 · x in {((2n+1)pi)/2, n in ZZ} If tan x = 1, then sin x = cos x. We know this is true for x = pi/4 as a base case. Now, the tangent function is periodic with it's period p = npi, where n is an integer. So tan x = tan (x+npi). Go back to the original equality : tan x = tan (x+npi) = 1 The first positive value x_0 for which tan x = 1 is, as stated before, pi/4. tan x_0 = tan(x_0 + npi) =1 …