How carry out you do these inquiries without a calculator? girlfriend don"t have to do castle all—I just need to know just how to perform at the very least one of them! ns appreciate any advice and/or solutions.
You are watching: Sin^-1(-sqrt 3/2)
There are a few values the $sin$ or $cos$ that you need to know, e.g. $sin(pi/3) = sqrt3/2$. Utilizing the fact that $sin$ is one odd function, $sin(-pi/3) = -sqrt3/2$. So $sin^-1(-sqrt3/2) = -pi/3$.
An equilateral triangle has all angles equal to $60^circ$. Let this triangle have a side size of $2$. Divide the triangle into two best triangles. One of the legs of the ideal triangle is of length $1$, the hypotenuse is of size $2$, and also from the Pythagorean theorem, the various other leg is of size $sqrt3$. From this we get $sin(60^circ)=fracsqrt32$. You have the right to use this triangle to discover the values of the trigonometric attributes of $30^circ$ and $60^circ$.
For trigonometric functions of $45^circ$, usage an isosceles appropriate triangle.
There are easy-to-remember vales that the sine, cosine and tangent functions for 0, 30, 45, 60 and also 90 degrees:Sine: 0, $frac12$, $fracsqrt22$, $fracsqrt32$, 1 respectivelyCosine: turning back the above sequence that valuesTangent: 0, $frac1sqrt3$, 1, $sqrt3$, $infty$
Then you must remember just how each of their graphs look at like, their linked symmetry relations and their reciprocal functions. Climate you can work the end the worths of these inverse attributes you have here.
For example, the first question asks for x whereby $sin x=-fracsqrt32$. Due to the fact that the sine role is odd, $sin(-x)=fracsqrt32$ and so x is $-60°$ ($-fracpi3$ radians).
You space clear on just how to do these questions. Thus in this answer, no explanation is necessary. Specifically answers will certainly be provided. Right here there are:
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NOTE: If among the answers over happen to be incorrect, can someone it is in kind sufficient to notify me? say thanks to you an extremely much!
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Discrepancy in differentiating: $y= an^-1left(fracsqrt1+sinx+sqrt1-sinxsqrt1+sinx-sqrt1-sinx ight)$
number of solutions come $cosleft(A cosleft(fracsA ight) ight) = sinleft(A cosleft(fracsA ight) ight)$
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