Trigonometry

The sea level as the tide goes in and out. An oscillating spring.

A vibrating string.

An obtuse angle does have a measure of over 90 degrees but it is also less than 180 degrees.

If tan 3a is equal to sin cos 45 plus sin 30, then the value of a = 0.4.

It is: cos = adj/hyp and the acute angles for the given right angle triangle are 67.38 degrees and 22.62 degrees

Putting more details in the answer means nobody sees the question as unanswered to attempt to answer it.

A sin curve varies evenly either side of the x-axis; the graph varies between -3.5 and +5.5; the mid-point of -3.5 and +5.5 is (5.5 - 3.5) ÷ 2 = 1

→ it has been shifted up the y-axis by 1 unit

→ k = 1

As the curve has been shifted up the y-axis by 1 unit, it varies from (-3.5 -1) = -4.5 to (5.5 - 1) = +4.5

The sin curve varies between -1 and +1

→ it has been stretched by 4.5

→ a = 4.5

Using the points with y-coordinate of 1, the curve is negative between the first two and positive between the second two; thus half the sine curve, (ie between 0 and π radians) is between two of them.

Between the first two of (-5.495, 1) and (0.785, 1) is 0.785 - -5.495 = 6.28 = 2 × 3.14 = 2π

Similarly between the second two of (0.785, 1) and (7.065, 1) is 7.065 - 0.785 = 6.28 = 2 × 3.14 = 2π

→ the x-axis has been stretched by 2π ÷ π = 2

→ b = 2

The sine curve starts increasing from zero, thus (0.785, 1) was originally at the origin (0, 0)

→ the curve has been shifted right by 0.785 = π/4

→ h = π/4

Thus the curve has equation:

y = 4.5 sin (2(x - π/4))

1 revolution = 2*pi radianstherefore, k revs per second = 2*k*pi radians per second

or

if you still work in degrees, it is 360*k degrees per second.

The smallest angle of the triangle will be opposite the smallest side and using the cosine rule it works out as 17.9 degrees rounded to one decimal place.

If the angles are the same and the sides are proportional by ratio then they are said to be similar triangles.

Yes because the given dimensions comply with Pythagoras; theorem for a right angle triangle.

If you mean a rectangle then its diagonal using Pythagoras; theorem is 2 times the square root of 41 or about 12.806 feet rounded to 3 decimal places.

csc θ = 1/sin θ

→ sin θ = -1/4

cos² θ + sin² θ = 1

→ cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4

In Quadrant III both cos and sin are negative

→ cos θ= -(√15)/4

The first angle is 166 deg and the second is 14 deg.

tan θ = sin θ / cos θ

sec θ = 1 / cos θ

sin ² θ + cos² θ = 1 → sin² θ - 1 = - cos² θ

→ tan² θ - sec² θ = (sin θ / cos θ)² - (1 / cos θ)²

= sin² θ / cos² θ - 1 / cos² θ

= (sin² θ - 1) / cos² θ

= - cos² θ / cos² θ

= -1

If you mean quadrilateral ABCD then by using Pythagoras' theorem diagonal AC is 5 cm and using the cosine rule angle ADC works out as 41.04 degrees.

1/4 of 360 degrees = 90 degrees which is a right angle

Using the sine rule you can find the other two sides:

Final angle = 180° - (37.25° + 48.4°) = 94.35°

→ other two sides are opposite the 37.25° and 48.4° angles as the longest side is opposite the largest angle.

→ the other two sides are:

s1/sin 37.25° = 162mm / sin 94.35° → s1 = 162mm × sin 37.25°/sin 94.35°

and s2 = 162mm × sin 48.4°/sin 94.35°

→ the perimeter = 162mm + 162mm × sin 37.25°/sin 94.35° + 162mm × sin 48.4°/sin 94.35°

= 162mm (1 + (sin 37.25° + sin 48.4°)/sin 94.35°)

≈ 382 mm

It's the statement that in any triangle, the sum of the lengths of any two sides must be greater or equal to the length of the third side.

The answer is 0.2867.

If you mean trigonometry then it is the working properties of triangles.

The question asks about the "indicated operations". In those circumstances would it be too much to expect that you make sure that there is something that is indicated?

csc(x)*{sin(x) + cos(x)} = csc(x)*sin(x) + csc(x)*cos(x)

=1/sin*(x)*sin(x) + 1/sin(x)*cos(x) = 1 + cot(x)

For a right angle triangle the trigonometrical ration is: tangent = opposite/adjacent

180 degrees = pi radians( 3.141592.... radians) .

Hence

216/180 = x radians / pi radians.

Algebraically rearrange

x radians = 216 x pi / 180

x = 3.769911.... radians