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## Vectors Test… oh my

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**Vectors Test… oh my**• Class Average was 51% • We are re-evaluating how much we will count it for. • I will have your marks next week. • MOVING ON! Forget about what happened and let’s start fresh**TRIGONOMETRY**Trig Ratios of Right Angle Triangles Section 5.1**Review…**The acute angles of a right angle triangle are complementary, which means: angleA + angleB = 90˚ A c b C B a**Review…**Side c is called the hypotenuse A c b C B a**Review…**SOH CAH TOA!!!!! cosA = adjacent = b hypotenuse c A c b C B a**Review…**SOH CAH TOA!!!!! sinA = opposite = a hypotenuse c A c b C B a**Review…**SOH CAH TOA!!!!! tanA = opposite = a adjacent b A c b C B a**3 New Ratios**Secant (sec), cosecant (csc) and cotangent (cot) We can get these ratios by inverting the three ratios that we already know… A c b C B a**Secant is the inverse of cosine.**secA = 1 = hypotenuse = c cosA adjacent b A c b C B a**Cosecant is the inverse of sine.**cscA = 1 = hypotenuse = c sinA opposite a A c b C B a**Cotangent is the inverse of tangent.**cotA = 1 = adjacent = b tanA opposite a A c b C B a**Example 1**• Find all sinA, cosA, tanA, secA, cscA, tanA First, you need to findthe hypotenuse! a2 + b2 = c2 32 + 42 = c2 c = 5 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA sinA = opp = 4 hyp 5 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA cosA = adj = 3 hyp 5 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA tanA = opp = 4 adj 3 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA secA = hyp = 5 adj 3 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA cscA = hyp = 5 opp 4 A 5 3 C B 4**Example 1**Find ratios sinA, cosA, tanA, secA, cscA, tanA cotA = adj = 3 opp 4 A 5 3 C B 4**Another Useful Ratio…**tanA = sinA cosA And so… cotA = cosA sinA**Remarkable Angles**• Look at workbook p.191-192. Take 10 minutes to do Activity 2. THERE WILL BE MORE NOTES so do not change spots.**Remarkable Angles**Notice that for - 0˚ and 90˚, sine and cosine are opposite - 30˚ and 60˚, sine and cosine are opposite**Example 2**Using the chart, find the exact values of x and y sin30˚= 1 2 1 = opp 2 hyp 1 = x 2 10 x = 5 A 10 x 30˚ C y B Cross Multiplyand simply**Example 2**Using the chart, find the exact values of x and y cos30˚= √3 2 √3 = adj 2 hyp √3 = y 2 10 x = 5√3 A 10 x 30˚ C y B Cross Multiplyand simply**HOMEWORK**Workbook p.191 #1a, 2 (solve means find all sides and all angles) p.193 #3,4