Q:

PLEASE HELP IMMEDIATELY!! will MARK BRAINLIEST AND GIVE 16 POINTS! (multiple choice but please try to show steps)1.Given that 0∘≤C≤180∘, determine the value(s)of ∠C to the nearest degree when sinC=0.9848.A) 80°, 100°B)100°C)10°, 80°D)80°2. θ is an angle in standard position whose terminal arm is inquadrant IV and cosθ=3/sqrt(13). Find cscθ.A)−2/Sqrt(13)B)−4/Sqrt(13)C)−Sqrt(13)/2D)Sqrt(13)/43.If secθ=−52, and sinθ>0, what is the value of tanθ?A) −Sqrt(21)/2B)Sqrt(−21)C)−2 Sqrt(21)/21D)−5 sqrt(21/ 21

Accepted Solution

A:
Answer:1. The values of angle C to the nearest degree are 80° , 100° ⇒ (A)2. csc Ф = -(√13)/2 ⇒ (C)3. tan Ф = - (√21)/2 ⇒ (A)Step-by-step explanation:* Lets explain how to solve the problem1. ∵ The measure of angle C is ⇒ 0° ≤ m∠C ≤ 180°∴ ∠C lies in the first quadrant or in the second quadrant∴ m∠C = Ф OR  m∠C = 180 - Ф, where Ф is an acute angle∵ sin∠C = 0.9848∴ sin Ф =  0.9848- Use the inverse function sin^-1 to find Ф∴ Ф = sin^-1 0.9848∴ Ф ≅ 80°- Lets find ∠C∵ m∠C = Ф∴ m∠C = 80°∵ m∠C = 180° - Ф∴ m∠C = 180 - 80 = 100°* The values of angle C to the nearest degree are 80° , 100°2.- The terminal arm of angle Ф is in  quadrant IV∵ In quadrant IV sin Ф , csc Ф , tan Ф , cot Ф are negative values∵ In quadrant IV cos Ф , sec Ф are positive values∵ cos Ф = 3/√13∵ csc Ф = 1/(sin Ф)- Lets use the identity sin²Ф + cos²Ф = 1 to find sin Ф∵ sin²Ф + (3/√13)² = 1∴ sin²Ф + 9/13 = 1 ⇒ subtract 9/13 from both sides∴ sin²Ф = 4/13 ⇒ take √ for both sides∵ sin Ф = ± 2/√13- The value of the sin the IV quadrant is negative∴ sin Ф = - 2/√13∵ csc Ф = 1/sin Ф∴ csc Ф = -(√13)/23.∵ sec Ф = -5/2 and sin Ф > 0∵ sec Ф = 1/cos Ф- The value of cos Ф is negative and the value of sin Ф is positive,  then Ф lies in the second quadrant∵ In the second quadrant cos Ф , sec Ф , tan Ф , cot Ф are negative   values but sin Ф and csc Ф are positive values- Lets use the identity tan²Ф + 1 = sec²Ф to find tan Ф∵ sec Ф = -5/2∵ tan²Ф + 1 = sec²Ф∴ tan²Ф + 1 = (-5/2)²∴ tan²Ф + 1 = 25/4 ⇒ subtract 1 from both sides∴ tan²Ф = 21/4 ⇒ take √ for both sides∴ tan Ф = ± √21/2∵ Ф lies in the second quadrant∴ tan Ф = - (√21)/2