Choose three options which are true:
a) an angle of 150 degrees is equivalent to 2pie/3 radians.
b) Cos 0 = cos (0 – pie/2) for al values of 0.
c) Sin 0 = cos (0 – pie/2) for all values of 0.
d) If triangle ABC has a right angle at B, then sin A = cos C
e) In any triangle ABC, if the lengths of just two sides of the triangle are known, then you always calculate the third.
f) In any triangle ABC,AB sin C = AC sin B
g) If triangles PQR and XYZ are similar, with P = X, Q = Y, R = Z, then XY/PQ = XZ/PR
h) In any triangle PQR, cos R = PR^2 + PQ^2 – QR^2/ 2 x PR x PQ.
CAN ANY 1 HELP ME ON WHICH 3 OPTIONS ARE RIGHT??
Which have you eliminated? I takes just a min to go through each ansewer.
i think its d and e and i don't knw wat cod be the third option, is this ryt?
Based on your elimination of options d) and e), let's analyze the remaining options and determine which ones are true:
a) an angle of 150 degrees is equivalent to 2π/3 radians.
To verify this, we need to convert 150 degrees to radians. Since there are 180 degrees in π radians, we can set up a proportion:
180 degrees = π radians
150 degrees = (150/180)π radians
Simplifying, we get: 150 degrees = (5/6)π radians
Therefore, option a) is true.
b) Cos 0 = cos (0 - π/2) for all values of 0.
To verify this, we can apply the cosine difference identity, which states that cos (A - B) = cos A * cos B + sin A * sin B. In this case, A = 0 and B = π/2:
cos (0 - π/2) = cos 0 * cos (π/2) + sin 0 * sin (π/2)
cos (-π/2) = 1 * 0 + 0 * 1
cos (-π/2) = 0
Since cos (-π/2) = 0, option b) is true.
c) Sin 0 = cos (0 - π/2) for all values of 0.
To verify this, we can apply the sine difference identity, which states that sin (A - B) = sin A * cos B - cos A * sin B. In this case, A = 0 and B = π/2:
sin (0 - π/2) = sin 0 * cos (π/2) - cos 0 * sin (π/2)
sin (-π/2) = 0 * 0 - 1 * 1
sin (-π/2) = -1
Since sin (-π/2) = -1, option c) is false.
f) In any triangle ABC, AB sin C = AC sin B.
This can be verified using the Law of Sines: a / sin A = b / sin B = c / sin C, where a, b, and c are the lengths of the sides opposite angles A, B, and C, respectively. In this case, we are comparing sides AB and AC to the corresponding sine values:
AB / sin C = AC / sin B
Since this equation satisfies the Law of Sines, option f) is true.
g) If triangles PQR and XYZ are similar, with P = X, Q = Y, R = Z, then XY / PQ = XZ / PR.
Similar triangles have corresponding sides in proportion. In this case, we can compare sides XY and XZ to the corresponding sides PQ and PR:
XY / PQ = XZ / PR
Since this equation satisfies the definition of similar triangles, option g) is true.
Based on the analysis, the three options that are true are a), b), and g).