Search & Filtering
A. Solve the following problems. Write your answer on a sheet of paper.
1. Given that sin α = and sin β = , find 𝑡𝑎𝑛 (α + β) if both α and β are in QIV.
2. Given that csc A = , A in QI, and sec B = , sin B < 0, find
a. cos (A – B)
b. tan (A – B)
3. If tan (x + y) = and tan y = , what is tan x?
4. The point (9, –5) lies on the terminal side of the angle 𝜃 in standard position. Find (sin 𝜃 + cos 𝜃).
B. Solve the following problems. Write your answer on a sheet of paper.
1. If cos t = , what is cos 2t?
2. Use half – angle identities to find the exact value of tan 22.50 and sin 150.
1. Given that csc A = , A in QI, and sec B = , sin B < 0, find
a. cos (A – B)
b. tan (A – B)
1. Given that sin α = and sin β = , find 𝑡𝑎𝑛 (α + β) if both α and β are in QIV.
Determine the location from the surface of a vertical square so that the center of pressure will be acting 80mm below its center of gravity. Calculate as well the hydrostatic force exerted by oil. One side of the gate measures 2m.
Is 1 + x + [x /(1 )] /(1 ) an identity or equation? Explain by
2 − x = 1 − x
giving at least 2 example solutions.
Content of salt in 1 degre of hardness if water
Compute the curve data for the following arc definition curve. Given: the PI at station 26+31.25, a back tangent bearing from the PI to the PC of S25º36’24”W, a forward tangent from the PI to the PT of S37º46’48”E, and a tangent length of 436.18’. Calculate R, L, C, Delta, PC & PT (back & ahead) stations.
Problem solving involving inverse of sine
1.) Find the angle of inclination when balloon which is 170 m above the ground is connected to a meterological station by cable of length 200 m.
2) If a kite is 40ft. Off the ground and the string holding the kite is 42 ft long, what is the angle of elevation to the kite?
Problem involving cosine functions
1.) The top of a broken tree touches the ground at a distance of 15 feet from its base. If the length of the broken part is 17.4 feet, what angle does the broken end of the tree make with the ground?
2.) A 5 m ladder is leaned against a perpendicular wall such that its base is 2 m from the wall. Work out the angle between the ladder and the floor, giving your answer to two decimal places.
Problem involving inverse of tangent function
1.) Find the measures of angle of elevation of the top of the building which is 110 ft.high and Michael is 90 feel away from the base of the building.
2.) A ladder is placed against a 40 food high electric pole such that it touches the top of the pole. If the bottom of the ladder is 10 feet ayaw from the base of the pole, what angle does the bottom of the ladder make with the ground?
Simple trigonometry equation
Solve trigonometric equation
1) 3 tan² x - 1 = 0
2) 2 cos x + 1 = 0
3) 2cos²-cos x - 1 = 0
4) 2cos² x - 3cos x + 1 = 0
Explain TWO (2) example of facilities that are effectively involve in Best Management Practice (BMPs) to control stormwater quality.
