trig final

Find the quadrant in which 𝜃 lies from the information given. sin(𝜃) < 0 and cos(𝜃) > 0 sin(𝜃) < 0 and cos(𝜃) < 0 sec(𝜃) > 0 and tan(𝜃) < 0 tan(𝜃) < 0 and sin(𝜃) < 0

IV III IV IV

A 680-ft rope anchors a hot-air balloon as shown in the figure. (a) Express the angle 𝜃 as a function of the height h of the balloon. (b) Find the angle 𝜃 if the balloon is 610 ft high. (Round your answer to one decimal place.)

𝜃 sin^-1 (h/680) b. sin^-1 (610/680) then answer to degrees

cos (13𝜋/15) cos (-𝜋/5) - sin(13𝜋/15)sin (-𝜋/5) see pic evaluate in mW

(13𝜋/15) - (-𝜋/5)= 2𝜋/3

cos (45°) sec (45°)

1

sin 30° cos 60° + sin 60° cos 30°

1

From the top of a 280 foot lighthouse angle of depression to ship in ocean equals 21°. How far?

90-21= 69 280 ft x tan (69)=729

A ceiling fan with 24 inch blades rotate at 50 RPM. angular speed? linear speed?

angular speed 50 RPM x 2π= 100π linear speed 50 RPM x 2π x 24in=2400π

sin(𝜃) = − 15/17, 𝜃 in Quadrant IV cos(𝜃) = tan(𝜃) = csc(𝜃) = sec(𝜃) = cot(𝜃) = find the other trig values in quad IV

cos(𝜃) = 8/17 tan(𝜃) = -15/8 csc(𝜃) = -17/15 sec(𝜃) = 17/8 cot(𝜃) = -8/15

determine if angles are coterminal 5π/6, 17π/6 17-5 = or if difference in angles is

if equal 2π coterminal 360 = coterminal

15. y = −3 cos(5𝜋x) amp= 3 per= 2𝜋/5𝜋

see pic

Use an appropriate Half-Angle Formula to find the exact value of the expression. Simplify using half angle formula

see pic

To find the distance across a river, a surveyor chooses points A and B, which are x = 200 ft apart on one side of the river (see the figure). She then chooses a reference point C on the opposite side of the river and finds that ∠BAC ≈ 82° and ∠ABC ≈ 52°. Approximate the distance from A to C. (Round your answer to the nearest foot.)

see pic 180 -(82+52)= 46 left over angle

9. find x on triangle see pic

sin 30°= x/21

17. mound 2𝜋 + mound (2𝜋-->4𝜋) 2𝜋 = 4𝜋

y= 3 sin (1/2 x) see pic

16. add 𝜋/6 and 𝜋/2 to get period amp is top horizontal shift = 0

y= 5/2 cos (3x)