1:2:1 Maths Tuition

Special Trig Equation.....

Query:  How do I set about solving  sinθ + 2 cosθ  = 1?

Response:

 

Another Trig. Equation To Solve.....

Query: If 8cos²x+2sinx=7, find all the values of x in the range 0 to 360 degrees.

Response:

How Do I Get From A To C?

Query: Describe fully the transformation which takes shape A onto shape C. [Please click on the graphic to see the full size question].

Response: It can be seen that the shape A has been turned to arrive at position C, so a favoured method is to use tracing paper to investigate it further.

Proceed as follows: Trace the shape A and place it directly over A. Now put your pencil point on the point (0,0) and rotate the paper. Does the shape A cover position C? In this case it does, but in another question you would have to try other 'centres' with your pencil point, until one works.

You'll see that the transformation which maps A onto C is a clockwise rotation of 90^o centered at the origin (0,0).

Awkward Pythagoras Theorem Question...

Query: Triangle PQR is right angled at Q. The length of PR = 23.6 cm, the length of PQ is x cm and the length of QR is 6.2 cm longer than PQ. Write down and solve a quadratic equation to find the length of PQ correct to 1 decimal place.

Response: Please click on the graphic below to view the solution.

Angles In Circles...

Query [from Loopy]: How do I find angle OBD in this GCSE Higher question?

Response: The solution is supplied below (opens in new window):

Too Much Information?

Query [from TT]: I've got a find the angles with letters and every line seems to be equal to something else. I don't know where to start...

Response: Think of the diagram as 3 connected triangles...

• The right triangle is isosceles and has 1 known angle
• The middle triangle is equilateral
• The left triangle is isosceles but has two unknown angles

Download Full Solution [pdf]

One Tread At A Time...

Query [from RF]: An 8m ladder rises 7m against a vertical wall. What's the angle between the floor and the ladder?

Response: This is a strangely worded question and we must assume that the ground supporting the ladder is level and horizontal, to be able to apply right-angled trigonometry to the problem:

• Draw a simple sketch of the situation
• Mark the sides floor, wall and ladder
• Put the lengths 7 & 8 onto the diagram
• Indicate the right-angle
• Mark the angle between the floor & ladder with a letter
• Consider which sides are hypotenuse, opposite & adjacent
• Apply appropriate trigonometric ratio equation.

Download Solution [pdf]

A Negative Straight Line?

Query [from DJ99]: In the diagram the gradient of the straight line AB is -2 and the coordinates of point A are (8,0). How do you find the equation of AB?

Response: Start with y = mx + c, which is the general equation of all straight lines.

As m = -2, this becomes y = -2x + c.

Next, substitute the given point coordinates into this equation to find the value of 'c'.

Since x=8 & y=0, we get y = -2x + 16 as AB's equation.

NOTE: This can also be written in the form y + 2x -16 = 0.

Don't be put off by the negative gradient. It only means that in this line, as the values of x increase, the values of y decrease.

It's Pythagoras, Really...

Query [from PaulG]: I've been asked to find the distance from the point A(2,3) to another point B(5,-4) and I get the answer to be the square root of 10 when I apply the distance formula? What have I done wrong?

Response: The distance formula is actually an application of the Theorem of Pythagoras. If you draw a quick sketch of these points onto an X-Y coordinate grid, you'll get the picture that we've created here...

The X_AB shift is +3 units and the Y_AB shift is -7 units (not -1)

This means that AB² = 3² + (-7)² = 58, giving AB = √58.