Why does tan equal to sin/cos? - Socratic
Apr 15, 2015 · 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 ...
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.
Fundamental Identities - Trigonometry - Socratic
Here 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 …
What is #tan(45)#, #sin(45)# and #cos(45)#? - Socratic
Nov 17, 2017 · tan(45^@)=1 sin(45^@)=sqrt2/2 cos(45^@)=sqrt2/2 45^@ is a special angle, along with 30^@, 60^@, 90^@, 180^@, 270^@, 360^@. tan(45^@)=1 sin(45^@)=sqrt2/2 cos(45 ...
Double Angle Identities - Trigonometry - Socratic
Answer: 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 −tan2θ 1 +tan2θ. sankarankalyanam · 1 · Mar 9 2018.
Special Limits Involving sin(x), x, and tan(x) - Calculus - Socratic
For very small values of x, the functions \sin(x), x, and \tan(x) are all approximately equal. This can be found by using the Squeeze Law.
How do you simplify #cos(arctan(x)) - Socratic
Jul 26, 2016 · #cos a = 1/sqrt ( 1 + x^2 ), x in ( - pi/2, pi/2 )#. It is important that #cos a >= 0#, for #a in Q_1# or #Q_4#. If the piecewise-wholesome general inverse operator #(tan)^( - 1 ) # is used, #cos (tan)^(-1) x, = +-1/sqrt( 1 + x^2)# the negative sign is chosen, when #x in Q_3#. Example: #cos (arctan 1 ) = 1/sqrt 2, arctan 1 = pi/4.#
Half-Angle Identities - Trigonometry - Socratic
Half angle Identities in term of t = tan a/2. tana = 2t 1 − t2. Use of half angle identities to solve trig equations. Example. Solve cosx + 2 ⋅ sinx = 1 +tan(x 2). Solution. Call t = tan(x 2). Use half angle identities (2) and (3) to transform the equation. 1 − t2 4 + 1 +t2 4 = 1 + t.
Is sine, cosine, tangent functions odd or even? | Socratic
Feb 28, 2015 · y = cos x is always going to be even, because cosine is an even function. For example, cos #pi/4# in the first quadrant is a positive number and cos #-pi/4# (same as cos #pi/4#) in the fourth quadrant is also positive, because cosine is positive in quadrants 1 and 4, so that makes it an even function. (When comparing even and odd function, use ...
Prove that # cos A / (1- tan A) + sin A / (1- cot A) -= cos A - Socratic
Apr 24, 2017. We want to prove that. cosa 1 − tana + sina 1 − cota = cosa + sina. Rewrite the left using only sines and cosines: cosa 1 − sina cosa + sina 1 − cosa sina = cos2a cosa −sina + sin2a sina −cosa. Pulling a −1 out of the denominator of the second term gives us the same denominator: = cos2a cosa −sina − sin2a cosa ...