71. a. sin b. sin c. sin 72. a. cosl b. cos- c. cos! 73. а. агссоs (-1) b. arccos (0) 74. a. arcsin (–1) b. arcsin V2.

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: Let sin s=--, with s in quadrant IV and let cos %3D II. Find cach of the following. 4. cos (s +1) 5.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6. Suppose that sin(0) of sin(20). 15 and that the terminal side of 0 is in the second quadrant.…

A: The solution is:

Q: 4 Suppose that sine = and <0<. Find the exact values of cos and tan Cos Undefined tan Continue O

A:

Q: Suppose that places) < 0 < 2T, csc(0)=8/3, find sin(0)=___. 2 (round to 3 decimal

A:

Q: 4 Suppose that sin e -and <0<1. Find the exact values of cos 2 and tan 2. Cos 2. = D tan, 2) %3D

A: As we know sin2θ+cos2θ=1. cosθ=1-452=1-1625=-35 Using Double angle formula: sinθ2=1-cosθ2=1+352=810…

Q: 4.1- cos? 0 = sin 0cose tan 0

A:

Q: 2 | sin' O cos' OdO O cos

A: I have stated the used formula in the solution

Q: and π 6. If tan y = - <y<7, find sin

A: We have  tany=-115 and π2&lt;y&lt;π we have to find siny2=? by using half angle identity.

Q: - If 0 = then 3 sin(0) = cos(0) = CoS

A:

Q: 2 _ 2 if tane + sin0= m and tan0 – sin0 = n ,show that m² – n´ = 4 mn

A:

Q: If COS 0 = √√3 2 ო sino = 9=1/1/21 FIN O sin0 = 1/14 2 O sin0 ine=-2/2 O sine= 11/13 2 == and < 0<-…

A: topic- trigonometric ratios

Q: A = -, find sin 2. If 90° <0 < 180° and cos 0 :

A:

Q: If tan(0) Hint = sin(0) = cos(0) = sec (0) = 15 - 8 ) 0 ≤0 ≤ 90°, then the exact value of

A: Here we have to find the other trignometric function.

Q: If cos e = Find the value of cote + co sece.

A:

Q: Find sin cos 2 (3}))

A: We Have to solve above question

Q: 6) If sin 0 = 0.2774, find cos 0. Round to four decimal places.

A: Given: sinθ=0.2774

Q: 16 If sin 0 = find cos 0 and tan 0, 3 %3D

A: sinθ=63To find: tanθ,cosθ

Q: 2. cos(arctan(1)) =

A: cosarc cosx =x

Q: If sine= 2 and sece<0, find cose and tane 2/5 cos e= 2, tane= 3 -25 cose= 3 tan e= 5 5 O sece= 2/3,…

A:

Q: 4. If the sine ratio is given, then how can sin be determined?

A: if sine ratio is given. Find: How can sinθ2 be determined?

Q: Express cos { θ + π/2 ) and sin { θ + π/2 } ) in terms of cosθ and sinθ.

A: Given  cosθ+π2, sinθ+π2

Q: 2) Verify. cot8 ese 6 %3D sin 6 tan 6

A: Use the following identities:

Q: 20) If csc0 = 5 on a right triangle, find the sine; cos0; tan0. V11 A) sin0 = =; cose = 5/11 ; tan)…

A: We have to find sin θ, cos θ and tan θ where it is given that: cosec θ=65 We know that cosec…

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: If 0 17 then 3 sin(0) = %3D cos(0) = %3D Give exact values. No decimals allowed!

A:

Q: If 5 tana =4 5 sin a – 3 cosa 1 Show that 5 sin a + 2cos a 6.

A:

Q: 1. If theta = arcsin(1/2) and 90deg < theta < 270deg, what is tan theta? 2. Find the value of…

A:

Q: 3 and cos B = with a in QI and B in QII. 13 2. Find the exact value of sin(a - B) if sina = = --

A:

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

A:

Q: If csc(z) = 4, for 90° < z < 180°, then sin (;) - ()- cos tan

A:

Q: If 0 = – 3T then 4 sin(8) = %3D cos(0) = Give exact values. No decimals allowed!

A: Find the value

Q: 12. sin 2t – tan t = tant cos 2t - HINT: You will use a reciprocal identity.

A: use the formula

Q: 15 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in quadrant II. 17

A:

Q: 3 where sec 0<0: find the exact value for cos 5 . Given: sin 0 = %3D --

A: sinθ=-35  &amp;  secθ&lt;0 By using the identity sin2θ+cos2θ=1, we get…

Q: 1. If 0° <0< 90° and sin 0 = , find sin 20. %3D

A:

Q: cos 2(theta) if sin theta = 5/8

A: Here we have to find cosθ2 and cos2θ=? If sinθ=58 where 0≤θ≤π2

Q: 15 Find sin 2x, cos 2x, and tan 2x if cosx = 17 and x terminates in quadrant I.

A: Given that  cos x = 1517 and x terminates in quadrant I. We have to find  sin 2x, cos 2x, and tan…

Q: Find cos 0 and sin 0 if tan 0 = 4 and π &lt; 0 &lt; 3π /2.

A: We have to find cos θ and sin θ if tan θ=4 where π&lt;θ&lt;3π2. Since π&lt;θ&lt;3π2 therefore angle…

Q: sin(A+B) = sinA cosB + cosA sinB

A:

Q: 16. If 180° <0 <270° and cos (0) = then determine the exact values of sin(0) and tan(0).

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx = and x terminates in quadrant I. 5 sin 2.x cos 2.x tan 2.x

A:

Q: Suppose, for some angle 0 drawn in standard position, tan(e) = -24/7 and sin(0) < 0. Find the exact…

A:

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.