which value is greater sin 60 or cos 30?

Answer 1

The cosine of an angle is defined as the sine of the complementary angle. The complementary angle equals the given angle subtracted from a right angle, 90°. For instance, if the angle is 30°, then its complement is 60°. Generally, for any angle t,

cos t = sin (90° – t).
Written in terms of radian measurement, this identity becomes

cos t = sin (∏/2 – t).

Right triangles and cosines
Consider a right triangle ABC with a right angle at C.

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A = 30°, (90° - A) = 60°


Consider the triangle PQR (drawing) with all three angles equal to 60°. By symmetry, all three sides are equal too (a more rigorous proof exists, but we skip it). Drop a line QS perpendicular to PR: it divides the big angle into two right-angled triangles with sharp angles of (30°, 60°), which is the kind we are interested in. By symmetry, the triangles are of equal size and shape ("congruent") and therefore (skipping another proof)

SR = (1/2) PR
In the notation of the drawing


a = (1/2) c

a/c = 1/2 = sin 30° = cos 60°
Continuing
sin2 30° = 1/4
But
sin2 30° + cos2 30° = 1
So
1/ 4 + cos2 30° = 1
Subtract 1/4 from both sides

cos2 30° = 3/4

cos 30° = SQRT(3)/ SQRT(4) = SQRT(3)/2 = 1.7320508/2

cos 30° = 0.8660254 = sin 60°

so you see they are equal.

Good question and Good luck

Answer 2

If the 30 and 60 are in degrees, then they are equal. If they are in radians (which is the default), then sin 60 is larger.

Answer 3

They are equal.

sin(a) = cos(90 - a), so if a = 30 deg

sin(60) = cos(90 - 60), sin(60) = cos(30)

perhaps you must know that

sin(60) = cos(30) = sqrt(3)/2

Answer 4

Equal.

Answer 5

Equal.

Answer 6

both values are equal
sin60 = cos [90-@]
@=theta

therefore
sin60=cos[90-60]
sin60=cos30
hence proved

Answer 7

BOTH ARE EQUAL.
sin 60 =0.866
cos 30=0.866

Answer 8

in case you do degrees, they're both .886, and in case you do radians, this is sin60 = -.305 cos30= .154 in case you do not understand or you probably did not study radians in college, then purely flow with degrees and say they're both .886

Answer 9

Both are the same No questions about that!!

Answer 10

Hey!
they are equal if they are in degrees