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.

would it be D and E and F ??

e is obviously false.
d is true
f is not the law of sines I learned. AB is side c, and AC is side b.

c*SinC is not equal to b*SinB.

c/SinC= b/SinB is the law of sines.

The correct options that are true are:

d) If triangle ABC has a right angle at B, then sin A = cos C
g) If triangles PQR and XYZ are similar, with P = X, Q = Y, R = Z, then XY/PQ = XZ/PR

So, the correct options are d) and g).

Let's go through the options to determine which ones are true.

a) An angle of 150 degrees is equivalent to 2π/3 radians.
To convert degrees to radians, we need to multiply the angle in degrees by π/180. So, 150 degrees would be (150 * π/180) radians, which simplifies to 5π/6 radians. Therefore, option a is true.

b) Cos 0 = cos (0 - π/2) for all values of 0.
Using the cosine function, we know that cos(0) = 1. If we evaluate cos (0 - π/2), we get cos(-π/2), which is also equal to 1. Thus, option b is true.

c) Sin 0 = cos (0 - π/2) for all values of 0.
This statement is not true. The sine function and the cosine function are different, and their outputs are not always equal. Therefore, option c is false.

d) If triangle ABC has a right angle at B, then sin A = cos C.
When a triangle has a right angle at vertex B, it is known as a right triangle. In a right triangle, the sine of angle A would be equal to the cosine of angle C. Therefore, option d is true.

e) In any triangle ABC, if the lengths of just two sides of the triangle are known, then you can always calculate the third side.
This statement is false. With just the lengths of two sides of a triangle, you can only determine the length of the third side if you also have information about the angle(s) between the known sides. Therefore, option e is false.

f) In any triangle ABC, AB * sin C = AC * sin B.
This statement is known as the law of sines. It states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Therefore, option f is true.

g) If triangles PQR and XYZ are similar, with P = X, Q = Y, R = Z, then XY/PQ = XZ/PR.
When two triangles are similar, it means their corresponding angles are equal and their corresponding sides are proportional. In this case, if P, Q, R correspond to X, Y, Z respectively, then XY/PQ would be equal to XZ/PR. Therefore, option g is true.

h) In any triangle PQR, cos R = (PR^2 + PQ^2 - QR^2) / (2 * PR * PQ).
This statement is known as the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Therefore, option h is true.

Based on the explanations above, the correct options are a), b), d), f), g), and h).