+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHSCurrent Score : – / 115 Due : Sunday, February 7 2016 10:00 PM GST1. –/8.33 pointsSPreCalcINT6 7.1.004.Write the trigonometric expression in terms of sine and cosine, and then simplify.2. –/8.33 pointsSPreCalcINT6 7.1.016.Simplify the trigonometric expression.3. –/8.33 pointsSPreCalcINT6 7.1.022.Simplify the trigonometric expression.HW1 (Homework)Hamad Al Derei:HE$VVLJQcos t csc tcot xcsc(−x)cot x sin x sec x+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS4. –/8.33 pointsSPreCalcINT6 7.1.028.Consider the given equation.(a) Verify algebraically that the equation is an identity.This answer has not been graded yet.(b) Confirm graphically that the equation is an identity.This answer has not been graded yet.5. –/8.33 pointsSPreCalcINT6 7.1.036.Verify the identity.Use the Even­Odd Identities to rewrite the expression.Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine.Use a Pythagorean Identity to rewrite the expression in terms of a single function, and then simplify.cot y = csc y − sin ysec ycos(−Ƚ) cot(−Ƚ) + sin(−Ƚ) = −csc Ƚcos(−Ƚ) cot(−Ƚ) + sin(−Ƚ) =− sin Ƚ= − cos Ƚ − sin Ƚ=sin Ƚsin Ƚ= =sin Ƚ+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS6. –/8.33 pointsSPreCalcINT6 7.1.048.Verify the identity.Expand the product.Use the Reciprocal Identities, and then simplify.Use a Pythagorean Identity, and then simplify.(cot x − csc x)(cos x + 1) = −sin x(cot x − csc x)(cos x + 1) =cot x cos x + cot x − csc x cos x −=+ − −=cos2 xsin xcos xsin xcos xsin xsin x= =sin x+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS7. –/8.33 pointsSPreCalcINT6 7.1.052.Verify the identity.Use a Pythagorean Identity, and then simplify.8. –/8.33 pointsSPreCalcINT6 7.1.058.Verify the identity.Multiply the numerator and denominator by a common value, and then simplify.Use a Pythagorean Identity.2 sin2 x − 1 = 1 − 2 cos2 x2 sin2 x − 1 =2− 1=2 −− 1==cos x + 1cos x − 1−sin2 x(cos x − 1)2= =cos x + 1cos x − 1cos x + 1cos x − 1cos x − 1(cos x − 1)2=+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS9. –/8.33 pointsSPreCalcINT6 7.1.069.Verify the identity.Use the Reciprocal Identities, and simplify the compound fraction.cot x − csc x = cot x1 − sec x= = = = =cot x − csc x1 − sec x−1 −cos xsin x1sin x1cos x−1 −cos xsin x1sin x1cos xsin x cos xcos xsin x (cos x − 1)sin x+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS10.–/8.33 pointsSPreCalcINT6 7.1.078.Verify the identity.Use the Pythagorean and Reciprocal Identities to simplify.11.–/8.33 pointsSPreCalcINT6 7.1.082.Verify the identity.This answer has not been graded yet.sin2 t + cot2 t − 1 = cot2 tcos2 t= =+=+=+ csc2 t=sin2 t + cot2 t − 1cos2 t+ cot2 tcos2 t1cos2 tcos2 tsin2 t1cos2 t1sin2 tcot2 x − tan2 x = csc2 x − sec2 x+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS12.–/8.37 pointsSPreCalcINT6 7.1.092.Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7). Assume that13.–/1 pointsSPreCalcINT6 7.2.004.Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.14.–/1 pointsSPreCalcINT6 7.2.010.Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.15.–/2 pointsSPreCalcINT6 7.2.015.Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.Find its exact value.0 ≤ Ʌ < Ɏ/2.1 + x2, x = tan Ʌsin 255°cos 17Ɏ12sin 14° cos 16° + cos 14° sin 16°+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS16.–/1 pointsSPreCalcINT6 7.2.026.Prove the identity.This answer has not been graded yet.17.–/5 pointsSPreCalcINT6 7.2.021.Prove the cofunction identity using the Addition and Subtraction Formulas.Since is undefined, use a Reciprocal Identity, and then use the Substitution Formulas to simplify.cos x − Ɏ = sin x2tan Ɏ − u = cot u2tan Ɏ2tan − u == = = =Ɏ2sincos Ɏ − u2cos u − cos sin ucos cos u + sin sin uɎ2Ɏ2Ɏ2cos u − 0 sin u0 cos u + 1 sin usin u+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS18.–/1 pointsSPreCalcINT6 7.2.046.Write the given expression in terms of x and y only.19.–/1 pointsSPreCalcINT6 7.2.054.Evaluate the expression under the given conditions.tan(Ʌ + ;)ߖɅ in Quadrant III, sin ߖ ߖin Quadrant II20.–/1 pointsSPreCalcINT6 7.2.057.Write the expression in terms of sine only.sin(sin−1 x + cos−1 y)cos Ʌ = − 1 ,3 = ,123 sin 4Ɏx + 3 3 cos 4Ɏx+:KWWSVZZZZHEDVVLJQQHWZHE6WXGHQW$VVLJQPHQW5HVSRQVHVODVW”GHS21.–/2 pointsSPreCalcINT6 7.2.060.Consider the following equation.(a) Express the function in terms of sine only.(b) Graph the function.f(x) = sin x + cos xf(x) =