# If a=sin1230°, b=cos(-1150°), c=tan1670°, d=cos2260°, then which of the following ordering is correct? (A) c>a>b>d (B) c>b>a>d (C) a>c>b>d (D) a>b>c>d (E) none of the above

## both sin and tan are increasing functions in Quadrant I, and tan > sin

## a = sin30°

b = cos70° = sin20°

c = tan50°

d = -cos80°

sure looks like c > a > b > d

## How did you get to that conclusion?

## To determine the correct ordering, we need to evaluate the trigonometric functions for the given angles and compare the results.

Let's start by evaluating the trigonometric functions for each angle:

a = sin(1230°)

b = cos(-1150°)

c = tan(1670°)

d = cos(2260°)

Now, let's calculate the values for each trigonometric function:

a = sin(1230°)

Using the periodicity of the sine function, we can rewrite 1230° as 1230° - 360° = 870°. The sine of 870° is equal to the sine of (870° - 360°) = 510°. The sine of 510° is equal to the sine of (510° - 360°) = 150°. The sine of 150° is 0.5. Therefore, a = 0.5.

b = cos(-1150°)

Using the periodicity of the cosine function, we can rewrite -1150° as -1150° + 360° = -790°. The cosine of -790° is equal to the cosine of (-790° + 360°) = -430°. The cosine of -430° is equal to the cosine of (-430° + 360°) = -70°. The cosine of -70° is approximately 0.342. Therefore, b ≈ 0.342.

c = tan(1670°)

Using the periodicity of the tangent function, we can rewrite 1670° as 1670° - 180° = 1490°. The tangent of 1490° is equal to the tangent of (1490° - 180°) = 1310°. The tangent of 1310° is equal to the tangent of (1310° - 180°) = 1130°. The tangent of 1130° is approximately -0.886. Therefore, c ≈ -0.886.

d = cos(2260°)

Using the periodicity of the cosine function, we can rewrite 2260° as 2260° - 360° = 1900°. The cosine of 1900° is equal to the cosine of (1900° - 360°) = 1540°. The cosine of 1540° is equal to the cosine of (1540° - 360°) = 1180°. The cosine of 1180° is approximately -0.571. Therefore, d ≈ -0.571.

Now, let's compare the values:

c ≈ -0.886

a = 0.5

b ≈ 0.342

d ≈ -0.571

Comparing the values, we see that -0.886 < 0.5 < 0.342 < -0.571.

Therefore, the correct ordering is (A) c > a > b > d.