Trigonometry

I dont think it has uses in daily life..its just to find the area of a triangle

Example: Express sin 120⁰ as a function of an acute angle (an angle between 0⁰ and 90⁰).

Solution:

Each angle θ whose terminal side lies in quadrant II, III, or IV has associated with it an angle called the reference angle, alpha (alpha is formed by the x-axis and the terminal side).

Since 120⁰ lies on the second quadrant, then alpha = 180⁰ - 120⁰ = 60⁰.

Since sine is positive in the second quadrant, sin 120⁰ = sin 60⁰.


Example: Express tan 320⁰ as a function of an acute angle.

Solution:

Since 320⁰ lies on the fourth quadrant, then alpha = 360⁰ - 320⁰ = 40⁰.

Since tangent is negative in the fourth quadrant, tan 320⁰ = -tan 40⁰.

cos(-100 degrees)

It is because angles are measured counter-clockwise for the horizontal x-axis.

The second quadrant.

Mechanics use trigonometry to find angles mostly used in body or chassis work.

an impossible event has a probability of 0, it will never occur

a certain event has a probability of 1, it will always occur

.999 repeating = 1
So 1.0
think of it as
7/9 = .777...
8/9 = .888...
9/9 = .999... 9/9 = 1

When placed next to any angle on a triangle, the theta symbol (θ) represents that missing angle.

Name the rectangle ABCD,letting the larger side be AB(7cm) and the smaller side be AC(5cm). Draw the two diagonals across the rectangle. Name the point of intersection of the two diagonals (which resembles an X) F. Name the midpoint between the smaller side AC, to be E.

AFC is the acute angle you are looking for, angle AFE is half of that.

So AFE is a right angled triangle and AE is equal to half of 5cm, which is 2.5; FE is equal to half of 7cm, which is 3.5.

Now, taking triangle AFE,

Tan AFE=2.5/3.5

AFE=35.537 degrees

Since the angle AFE is half of the acute angle AFC that you are looking for,

multiply AFE into two

So, 35.537*2

=71.075 degrees

=71.1 degrees (to 1 decimal place)

AFC= 71.1 (ANS)

Use Pythagoras' Theorem - the hypothenuse of a right triangle is square root of (a2 + b2)

Use Pythagoras' Theorem - the hypothenuse of a right triangle is square root of (a2 + b2)

Use Pythagoras' Theorem - the hypothenuse of a right triangle is square root of (a2 + b2)

Use Pythagoras' Theorem - the hypothenuse of a right triangle is square root of (a2 + b2)

yes

Search on Google for free IGCSE past papers maths. You will get a number of sites: pick any. You will need to specify your board (Edexcel, CIE), and possibly the specification code.

y = 2*tan(2x) is an equation in two variable. There can be no answer. While x can be made the subject of the formula, that is not an *answer*.

He is 75 feet high.

The slope of a line tells a person what the rate of change is for a certain amount of time. For instance, on a graph where distance is the X axis and time is the Y axis, the slope will tell the velocity, literally, distance/time.

Putting a question mark at the end of a phrase does not make it a sensible of even an answerable question.

Sine and cosine of real numbers? Yes, they do exist. In fact, sines and cosines of complex numbers also exist. Does that answer the question?

It depends on your latitude. At the equator (0 degrees) a degree of longitude covers just over 111 km, so 8 degrees would be about 890 km.

At 45 degrees of latitude, a degree of longitude covers just under 79 km, so 8 degress would be about 555 km.

Check out the calculator in the related link. Enter the degrees of latitude and it gives the length of a degree at that point.

(tan x + cot x)/sec x . csc x

The key to solve this question is to turn tan x, cot x, sec x, csc x into the simpler form.

Remember that tan x = sin x / cos x, cot x = 1/tan x, sec x = 1/cos x, csc x = 1/sin x

The solution is:

[(sin x / cos x)+(cos x / sin x)] / (1/cos x . 1/sin x)

[(sin x . sin x + cos x . cos x) / (sin x . cos x)] (1/sin x cos x)

[(sin x . sin x + cos x . cos x) / (sin x . cos x)] (sin x . cos x)

then

sin x. sin x + cos x . cos x

sin2x+cos2x

=1

The answer is 1.

It is the total stopping time.

Cot(1.13 radians) = 0.4718

The volume.

Their sum must be 60.