Find the sin & Cos of O-180,-90,-45,45, 135) degree 0(-135, 0, 4o, 180) radian-

Q: Suppose the terminal side of an angle 0 passes through the point (-4,-5) when drawn in standard…

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Q: Divide 4 (cos 60° + i sin 60°) by 2 (cos 30° + i sin 30°) in rectangular form.

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Q: 4. The point (9, -5) lies on the terminal side of the angle e in standard position. Find (sin 0 +…

A: Use pythagorous theorem to solve

Q: 20. Prove that an angle of 0 radians is constructible if and only if the real number cose(sine)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Could you explain in detail how you got tan^3(theta) = 3. Thanks

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Q: Find tan 0 if sec 0 = ,/5 and sin 0 < 0.

A: We have given that;

Q: Find (ot (Sin-¹) (-1))

A: cotarcsin-36Use the following property: arcsin-x=-arcsinx=cot-arcsin36Use the following property:…

Q: Express the given sum or difference as a product of sines and/or cosines cos 2x+ cos 4x

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Q: Verify the identity: sec(α + β) = sec α sec β/(1 - tan α tan β)

A: Given sec(α + β) =secα secβ1- tanα tanβ∵sec θ = 1cos θ ; tan θ = sin θcos θ⇒ from (1) , we get…

Q: cos(3x) = 4 cos x – 3 cos x. COS

A: To Determine:  Use addition formulas and double angle formulas to verify the identity.  Given: we…

Q: Find sec- (7.9) (in radians). (Hint: Use cos-1)

A: To find:sec-17.9

Q: 79. Sin x = 2 +an 즐 14 tan'즉

A: Prove the identity Take RHS

Q: (-8,15)

A: Consider

Q: Find the values of sin 6 and tan if the point (-3, 4) is on the terminal side of @

A: We will use polar co-ordinate to find Trigonometric ratios

Q: Algebraically prove the identity, Left Side sin +1 1 sin 8-1 2 sec² 0. Right Side

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Q: Give expressions to represent all exact solutions to the equation in radians: sin: (x)-V3sin(x)=0

A: The given equation is sin2x-3sinx=0. Solve the above equation as follows.

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Given, sinθ.secθ=tanθ transform leftside to rightside from trignometric formula we know secθ=1cosθ…

Q: Express as a product.sin cos θ + sin 2 θ

A: To express sinθ cosθ+sin2θ. Solution: We know that, sin2θ=2sinθ cosθ Therefore, given expression can…

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: To verify the identity,  secθ-cos(θ)=tan(θ)sin(θ) Consider the left hand side of the equation,…

Q: Sketch 7 +4 sin 0 +3 cose

A: Let f(θ)=7+4sinθ+3cosθ .Rewrite the function into sine form only .…

Q: Explain how a right triangle can be used to find the exact value of sec (sin-1 4/ 5).

A: Given: secsin-145 for solving this, we assume sin-145=θsinθ=45                                   ..1…

Q: If sec theta = -4, find cos theta

A: Given  secθ=-4 To find cosθ  The identity used here cosθ=1secθ

Q: If  2sin2 theta  - cos2 theta = 2  then find the value of theta

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Q: find Cos0, tan0, and Sin0 if sec0=3 and 0 is acute.

A: To find the given values at an acute angle θ such that sec θ=3

Q: Solve for θ. Answer in radians. 6sin^2(θ)+sin(θ)-2=0

A: Explanation of the solution is given below...

Q: Find cos theta if (1, -3) is a point on the terminal side of theta -1/3

A: Given: 1,-3 is a point on the terminal side of θ. To find: cosθ Solution: Point 1,-3 is in quadrant…

Q: What is the exact value of cos x if the point (-4,2) lies on the terminal side of n angle x when…

A: Given: -

Q: Find the sine of ZU. 17 15 U 8 Write your answer as an integer or as a de sin (U) = %3D

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Q: Find sin a. (-/5 ,2) [ ?] 1

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Q: tan sin 8 (Simplify vour answer including

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Q: Find the sin & Cos of G (-180,-90,-445,45, 135) degree O(-135, 0, 90, 180) radian-

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Q: Find sin 20

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Q: Let (-4,5) be a point on the terminal side of 0 sin0= sec0= tan0=

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Q: Use 7.3 half angle formula to find sin θ/2 when tanθ=- 3/4 and 90<θ<180

A: Given: Now,

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Given : secθ-cosθtanθ = tanθsecθ

Q: Establish the identity. cos u tan u - sec u = 1+ sin u Write the left side in terms of sine and…

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Q: Write sin 41° in terms of cosine. sin 41° = = COS

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Q: The point (3, -2) lies on the terminal side of angle 0 . Find the exact value of sin 0 and cos O

A: We first sketch the situation roughly. Then we find the hypotenuse using Pythagorean theorem.…

Q: tan 45º cos 180° sin -30°

A: Given tan 45°we know that tanθ=sinθcosθtan 45°=sin 45°cos 45°=1212=1∴tan 45°=1

Q: True or False: cos(sin 0) = 1 and sin(cos0) = %3D

A: I have shown that given result is False.

Q: Find sin(2θ) if tan(θ) = 2/3

A: Consider the given trigonometric equation:

Q: 59. sin s= sece1 2sece 2.

A: Given that: sin2θ2=secθ-12secθ

Q: Establish the identity. sin 0. sec 0= tan 0 Write the left side in terms of sine and cosine. sin 0-[

A: Given,           sinθ·secθ=tanθ

Q: If sin(8) = -1/6, find sin(-0).

A: Given: sin(θ) -1/6   To determine: sin(-θ)

Q: Find the value of sec u if cos u = - 7

A: The sec and cos are important trigonometric functions. The other four functions are sine, tan, cot,…

Q: The terminal side of an angle theta in standard position intersects the unit at point (3/2, - 1/2)…

A: Given that point (3/2, -1/2). This is in the Cartesian plane and we find r and theta help of convert…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.