Click to start maths 4 Scotland www maths

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maths 4 Scotland www. maths 4 scotland. co. uk HIGHER MATHS Revision Angles greater than 90° Next

maths 4 Scotland www. maths 4 scotland. co. uk Definition of trigonometric functions hypotenuse opposite adjacent SOH – CAH - TOA A

maths 4 Scotland Problem: www. maths 4 scotland. co. uk What about angles > 90° We need a new definition for: sine cosine tangent

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Take a rotating line OP P (x, y) Let P be (x, y) Let length of OP be r r y Let be the angle between OP and OX O x X Define:

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Move OP to 2 nd quadrant Let P be (x, y) P (x, y) Let length of OP be r r y Let be the angle between OP and OX x O X Define: This is the same value as apart from x being negative

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Move OP to 3 rd quadrant Let P be (x, y) Let length of OP be r x O y Let be the angle between OP and OX X r Define: P (x, y) This is the same value as apart from x and y being negative

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Move OP to 4 rd quadrant Let P be (x, y) Let length of OP be r O Let be the angle between OP and OX x X r y P (x, y) This is the same value as apart from y being negative Define:

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Define: P (x, y) r + + + y O x X 1 st quadrant ALL x and y both positive r is always positive

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: + Define: P (x, y) r y - x O X 2 nd quadrant Sin x negative and y positive r is always positive 1 st quadrant ALL

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: - Define: x O y + X r 2 nd quadrant Sin P (x, y) x negative and y negative r is always positive Tan 3 rd quadrant 1 st quadrant ALL

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: - Define: + - x X O r y 2 nd quadrant 1 st quadrant Sin ALL Tan Cos P (x, y) x positive and y negative r is always positive 3 rd quadrant 4 th quadrant

maths 4 Scotland New Definition: All Sinners Take Care www. maths 4 scotland. co. uk Define: 2 nd quadrant 1 st quadrant Sin S ALL A Tan T Cos C 3 rd quadrant 4 th quadrant

maths 4 Scotland www. maths 4 scotland. co. uk New Definition: Define: 90 – 180° 180 – 270° 0 – 90° 270 – 360° 2 nd quadrant 1 st quadrant Sin, cos, tan of any angle between 0° and 360° S A is numerically the same as the acute angle between the rotating line and the x-axis T C but the sign (+ or -) is taken from ASTC 3 rd quadrant 4 th quadrant

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° = + sin 50° S A cos 290° tan 120° 50° sin 250° tan 100° cos 120° T C

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° cos 290° S A = + cos 70° tan 120° 70° sin 250° tan 100° cos 120° T C

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° S A cos 290° tan 120° = - tan 60° sin 250° tan 100° cos 120° T C

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° S A cos 290° tan 120° sin 250° tan 100° cos 120° = - sin 70° T C

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° S A cos 290° tan 120° 80° sin 250° tan 100° cos 120° = - tan 80° T C

maths 4 Scotland www. maths 4 scotland. co. uk Examples: sin 130° S A cos 290° tan 120° 60° sin 250° tan 100° cos 120° T = - cos 60° C

maths 4 Scotland Examples: www. maths 4 scotland. co. uk tan = 1 ignore the sign what is value of S A what is the acute value for 45° where is tan negative T C

maths 4 Scotland Examples: www. maths 4 scotland. co. uk sin = 0. 5 ignore the sign what is value of S A what is the acute value for 30° where is sin negative T C

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