Question

СРочно найти значение sin 72 *cos 12 - cos 72 * cos 78

Answer 1

Пишите градусы, а то можно подумать, что это в радианах!!!

$sin(72^{\circ})*cos(12^{\circ})-cos(72^{\circ})*cos(78^{\circ})= \\ \\ =\frac{1}{2}(sin(84^{\circ})+sin(60^{\circ}))- \frac{1}{2}(cos(-6^{\circ})+cos(150^{\circ}))= \\ \\ =\frac{1}{2}(sin(84^{\circ})+ \frac{ \sqrt{3} }{2} )- \frac{1}{2}(cos(6^{\circ})- \frac{ \sqrt{3} }{2})= \\ \\ =\frac{sin(84^{\circ})}{2}+ \frac{ \sqrt{3} }{4}- \frac{cos(60^{\circ})}{2}+ \frac{ \sqrt{3} }{4}= \frac{sin(84^{\circ})+ \sqrt{3}-cos(6^{\circ}) }{2} \\ \\ sin(90^{\circ}-6^{\circ})=sin84^{\circ} ; \;\;sin84^{\circ}=cos(6^{\circ}); \\ \\ \frac{cos(6^{\circ})+ \sqrt{3}-cos(6^{\circ}) }{2}= \boxed {\frac{ \sqrt{3} }{2}}$

Answer 2

Sure, let's calculate the value step by step:

1. First, we need to convert the angles from degrees to radians since trigonometric functions in most programming languages and calculators typically work with radians.

To convert from degrees to radians:

• Multiply degrees by π/180

So, sin(72°) = sin(72 * π/180) cos(12°) = cos(12 * π/180) cos(72°) = cos(72 * π/180) cos(78°) = cos(78 * π/180)

2. Now, let's find the values of each term using a calculator or approximation:

sin(72°) ≈ 0.9510565163 cos(12°) ≈ 0.9781476007 cos(72°) ≈ 0.3090169944 cos(78°) ≈ 0.2079116908

3. Now, substitute these values into the expression:

sin(72°) * cos(12°) - cos(72°) * cos(78°) ≈ 0.9510565163 * 0.9781476007 - 0.3090169944 * 0.2079116908

4. Calculate the result:

sin(72°) * cos(12°) - cos(72°) * cos(78°) ≈ 0.9300945661 - 0.0642392029

5. Finally, obtain the final value:

sin(72°) * cos(12°) - cos(72°) * cos(78°) ≈ 0.8658553632

So, the value of sin(72°) * cos(12°) - cos(72°) * cos(78°) is approximately 0.8659.