63: Inverse Trigonometric Functions
arcsin(O=H) = arccos(A=H) = arctan(O=A) = Right triangles can be usedto nd sine, cosine and tangent of an inverse trig function: 2 Draw a right triangle with
Inverse Trigonometric Functions
As will the arccsc x, arctan x and arccot x functions As will the arcsec x function Try these: sin-1 ( √3 ⁄ 2) cos-1(√3 ⁄ 2) tan-1 -1 sec-1-1 sin-1-sin-1 (-1/ 2) cos-1 0 cos-1 - tan-1 - √3 tan-1 (-1/√3 ) sec-1(-2/√3 ) sec-1 -√2 Some more complex problem involving arcsin, arccos and arctan: Hint: Draw a right triangle a) cos
Inverse Trigonometric Functions
y arcsin sin 1x: y cosx: y arccos x cos 1 x: arcsin( g) arctan( 3) h) tan 1( 3) 2 Find the measure of the a cute angles in a right triangle with a hypotenuse of
47 Inverse Trigonometric Functions
tan arctan 5 5 5 arcsin 5 sin cos cos 1 tan arctan 5 3 y 2, 2 arcsin sin y y arcsin sin 3 2 arcsin 1 2 3 2 x y f f 1 x x f 1 f x x x f f 1, Section 4 7 Inverse Trigonometric Functions 347 Activities 1 Evaluate Answer: 2 Use a calculator to evaluate Answer: 1 268 3 Write an algebraic expression that is equivalent to Answer: 3x 1 9x2 sin
Section 8 Inverse Trigonometric Functions
Solution: (a) Bythegeneralde &nitionofinversefunctions,y =arcsin ¡ 1 2 ¢ is the solution of the restricted Sine function for y : 1 2 =siny The words "restricted Sine" means that
17 ~ Inverse Trigonometric Functions
a) sec (arctan(-3/4)) b) cot(sin-1(-0 2)) c) A plane flies at an altitude of 6 miles toward a point directly over an observer Write the angle ø as a function of x, the horizontal distance from the observer to a point on the ground directly below the airplane
Some Worked Problems on Inverse Trig Functions
5 Simplify arccos(y)+arcsin(y): Solution Notice in the triangle in the gure below, that the sine of is yand the cosine of ˇ 2 is y x y 1 ˇ 2 So arcsin(y) = and arccos(y) = ˇ 2 Therefore arccos(y)+arcsin(y) = +(ˇ 2 ) = ˇ 2: Indeed, the expression arccos(y)+arcsin(y) merely asks for the sum of two complementary angles By de nition, the
47 Solving Problems with Inverse Trig Functions
(b)Notice in the triangle in Figure 35 that the sine of is yand the cosine of ˇ 2 is y So arcsin(y) = and arccos(y) = ˇ 2 Therefore arccos(y) + arcsin(y) = + (ˇ 2 ) = ˇ 2: Indeed, the expression arccos(y) + arcsin(y) merely asks for the sum of two complementary angles By de nition, the sum of two complementary angles is ˇ 2
Right Triangle Trig - 3rPrep
Arcsin — Arccos — Arc tan Arccot — Arccsc 17 For an angle with measure in a right triangle, and tan What is the value Of sin COs ? 12 319 29 For right triangle AABC shown below, which Of the following expressions has a value that is equal to cos A ? 9 feet c 15 feet 12 feet B c D E sin A sin B cos B tan A tan B B
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